Descriptor: "k-Set agreement" / Topic: k-set agreement - Searchworks@Jio Institute Digital Library Search Results

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38 results on '"k-Set agreement"'

1. Some New Results With k-Set Agreement

Author: Delporte-Gallet, Carole, Fauconnier, Hugues, Safir, Mouna, Goos, Gerhard, Series Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Castañeda, Armando, editor, Enea, Constantin, editor, and Gupta, Nirupam, editor
Published: 2024
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2. Optimal Algorithms for Synchronous Byzantine k-Set Agreement

Author: Delporte-Gallet, Carole, Fauconnier, Hugues, Raynal, Michel, Safir, Mouna, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Devismes, Stéphane, editor, Petit, Franck, editor, Altisen, Karine, editor, Di Luna, Giuseppe Antonio, editor, and Fernandez Anta, Antonio, editor
Published: 2022
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3. k-Immediate Snapshot and x-Set Agreement: How Are They Related?

Author: Delporte, Carole, Fauconnier, Hugues, Rajsbaum, Sergio, Raynal, Michel, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Woeginger, Gerhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Devismes, Stéphane, editor, and Mittal, Neeraj, editor
Published: 2020
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4. Set Agreement and Renaming in the Presence of Contention-Related Crash Failures

Author: Durand, Anaïs, Raynal, Michel, Taubenfeld, Gadi, Hutchison, David, Series Editor, Kanade, Takeo, Series Editor, Kittler, Josef, Series Editor, Kleinberg, Jon M., Series Editor, Mattern, Friedemann, Series Editor, Mitchell, John C., Series Editor, Naor, Moni, Series Editor, Pandu Rangan, C., Series Editor, Steffen, Bernhard, Series Editor, Terzopoulos, Demetri, Series Editor, Tygar, Doug, Series Editor, Weikum, Gerhard, Series Editor, Izumi, Taisuke, editor, and Kuznetsov, Petr, editor
Published: 2018
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5. Consensus Variants: Simultaneous Consensus and k-Set Agreement

Author: Raynal, Michel and Raynal, Michel
Published: 2018
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6. t-Resilient Immediate Snapshot Is Impossible

Author: Delporte, Carole, Fauconnier, Hugues, Rajsbaum, Sergio, Raynal, Michel, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, and Suomela, Jukka, editor
Published: 2016
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7. Black Art: Obstruction-Free k-set Agreement with |MWMR registers| < |proccesses

Author: Delporte-Gallet, Carole, Fauconnier, Hugues, Gafni, Eli, Rajsbaum, Sergio, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Gramoli, Vincent, editor, and Guerraoui, Rachid, editor
Published: 2013
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8. Simultaneous Consensus vs Set Agreement: A Message-Passing-Sensitive Hierarchy of Agreement Problems

Author: Raynal, Michel, Stainer, Julien, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Moscibroda, Thomas, editor, and Rescigno, Adele A., editor
Published: 2013
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9. Renaming Is Weaker Than Set Agreement But for Perfect Renaming: A Map of Sub-consensus Tasks

Author: Castañeda, Armando, Imbs, Damien, Rajsbaum, Sergio, Raynal, Michel, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, and Fernández-Baca, David, editor
Published: 2012
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10. Easy Impossibility Proofs for k-Set Agreement in Message Passing Systems

Author: Biely, Martin, Robinson, Peter, Schmid, Ulrich, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Fernàndez Anta, Antonio, editor, Lipari, Giuseppe, editor, and Roy, Matthieu, editor
Published: 2011
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11. Relations Linking Failure Detectors Associated with k-Set Agreement in Message-Passing Systems

Author: Mostéfaoui, Achour, Raynal, Michel, Stainer, Julien, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Défago, Xavier, editor, Petit, Franck, editor, and Villain, Vincent, editor
Published: 2011
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12. The Universe of Symmetry Breaking Tasks

Author: Imbs, Damien, Rajsbaum, Sergio, Raynal, Michel, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Kosowski, Adrian, editor, and Yamashita, Masafumi, editor
Published: 2011
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13. Optimal algorithms for synchronous Byzantine k-set agreement.

Author: Delporte-Gallet, Carole, Fauconnier, Hugues, Raynal, Michel, and Safir, Mouna
Subjects: *STATISTICAL decision making
Abstract: This article is on k -set agreement (k SA) in an n -process synchronous message-passing system in which up to t processes can commit Byzantine failures. k SA is a decision problem in which at least each correct (i.e., non-Byzantine) process is assumed to propose and decide a value such that at most k different values are decided by the correct processes, in such a way that, if all the correct processes propose the same value v , they will decide v. This article investigates the possibility/impossibility domain of k SA in the presence of Byzantine processes. To this end it first extends a previous result and shows that k SA cannot be solved when (n < 2 t + t k) ∧ (n − t ≥ k + 1). On the positive side, it presents two synchronous round-based algorithms that solve Byzantine k SA. These algorithms are optimal with respect to the value of k and the number of rounds. The first algorithm is a one-round algorithm that has two instances. The first assumes n > 2 t + 1 and solves k SA for k ≥ ⌊ n − t n − 2 t ⌋ + 1 , while the second assumes n ≤ 2 t + 1 and solves k SA for k ≥ t + 1 (so this second case does not require a majority of correct processes). The second algorithm is based on two new notions denoted Square and Regions that allow each correct process to locally build a global knowledge on which processes proposed which values. This algorithm has also two instances. The first assumes n = 3 t and solves 2SA. The second assumes 2 t + 1 < n ≤ 3 t and solves k SA where k = n − t n − 2 t is an integer. It is worth noticing that the results presented in this article "almost" complete the possibility/impossibility cartography of k SA in synchronous Byzantine systems. The only case that remains open is when n − t n − 2 t is not an integer. • Optimal algorithms for k-set agreement in synchronous systems where some processes are Byzantine • Statement of non-trivial impossibility results • Knowledge-based algorithms • Introduction of new proof-oriented concepts (Squares and Regions) • Round Optimal algorithms (1 & 2 rounds) [ABSTRACT FROM AUTHOR]
Published: 2023
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14. Reaching agreement in the presence of contention-related crash failures.

Author: Durand, Anaïs, Raynal, Michel, and Taubenfeld, Gadi
Subjects: *SYSTEM failures
Abstract: While consensus (and more generally agreement problems) is at the heart of many coordination problems in asynchronous distributed systems prone to process crashes, it has been shown to be impossible to solve in such systems where processes communicate by message-passing or by reading and writing a shared memory. Hence, these systems must be enriched with additional computational power for consensus to be solved on top of them. This article presents a new restriction of the classical basic computational model that combines process participation and a constraint on failure occurrences that can happen only while a predefined contention threshold has not yet been bypassed. This type of failure is called λ-constrained crashes , where λ defines the considered contention threshold. It appears that when assuming such contention-related crash failures and enriching the system with objects whose consensus number is x ≥ 1 , consensus for n processes can be solved for any n ≥ x assuming up to x failures. The article proceeds incrementally. It first presents an algorithm that solves consensus on top of read/write registers if at most one crash occurs before the contention threshold λ = n − 1 has been bypassed. Then, the article considers two extensions. The first one assumes that the system is enriched with objects whose consensus number is x ≥ 1 , and shows that when λ = n − x , consensus can be solved despite up to x λ -constrained crashes, for any n ≥ x , and when λ = n − 2 x + 1 , consensus can be solved despite up to 2 x − 1 λ -constrained crashes, assuming x divides n. The second extension prolongs the previous results to the k -set agreement problem (which is a natural generalization of consensus). Impossibility results are also presented for the number of λ -constrained failures that can be tolerated. [ABSTRACT FROM AUTHOR]
Published: 2023
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15. Weakening Failure Detectors for k-Set Agreement Via the Partition Approach

Author: Chen, Wei, Zhang, Jialin, Chen, Yu, Liu, Xuezheng, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, and Pelc, Andrzej, editor
Published: 2007
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16. Strongly Terminating Early-Stopping k-Set Agreement in Synchronous Systems with General Omission Failures

Author: Parvédy, Philippe Raïpin, Raynal, Michel, Travers, Corentin, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Dough, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Flocchini, Paola, editor, and Gąsieniec, Leszek, editor
Published: 2006
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17. Early-Stopping k-Set Agreement in Synchronous Systems Prone to Any Number of Process Crashes

Author: Parvedy, Philippe Raipin, Raynal, Michel, Travers, Corentin, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Dough, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, and Malyshkin, Victor, editor
Published: 2005
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18. Solving k-Set Agreement Using Failure Detectors in Unknown Dynamic Networks.

Author: Jeanneau, Denis, Rieutord, Thibault, Arantes, Luciana, and Sens, Pierre
Subjects: *DYNAMICAL systems, *STANDARDS, *ALGORITHMS, *COMMUNICATION, *GRAPHIC methods
Abstract: The failure detector abstraction has been used to solve agreement problems in asynchronous systems prone to crash failures, but so far it has mostly been used in static and complete networks. This paper aims to adapt existing failure detectors in order to solve agreement problems in unknown, dynamic systems. We are specifically interested in the k-set agreement problem. The problem of k-set agreement is a generalization of consensus where processes can decide up to k different values. Although some solutions to this problem have been proposed in dynamic networks, they rely on communication synchrony or make strong assumptions on the number of process failures. In this paper we consider unknown dynamic systems modeled using the formalism of Time-Varying Graphs, and extend the definition of the existing \Pi \Sigma x,y failure detector to obtain the \Pi \Sigma \bot, x,y failure detector, which is sufficient to solve k-set agreement in our model. We then provide an implementation of this new failure detector using connectivity and message pattern assumptions. Finally, we present an algorithm using \Pi \Sigma \bot, x,y to solve k-set agreement. [ABSTRACT FROM AUTHOR]
Published: 2017
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19. Distributed Universality.

Author: Raynal, Michel, Stainer, Julien, and Taubenfeld, Gadi
Subjects: *DISTRIBUTED computing, *ALGORITHMS, *SEQUENTIAL analysis, *SYNCHRONIZATION, *SYSTEM analysis
Abstract: A notion of a universal construction suited to distributed computing has been introduced by Herlihy in his celebrated paper ' Wait-free synchronization' (ACM Trans Program Lang Syst 13(1):124-149, 1991). A universal construction is an algorithm that can be used to wait-free implement any object defined by a sequential specification. Herlihy's paper shows that the basic system model, which supports only atomic read/write registers, has to be enriched with consensus objects to allow the design of universal constructions. The generalized notion of a k -universal construction has been recently introduced by Gafni and Guerraoui (Proceedings of 22nd international conference on concurrency theory (CONCUR'11), Springer LNCS 6901, pp 17-27, 2011). A k-universal construction is an algorithm that can be used to simultaneously implement k objects (instead of just one object), with the guarantee that at least one of the k constructed objects progresses forever. While Herlihy's universal construction relies on atomic registers and consensus objects, a k-universal construction relies on atomic registers and k-simultaneous consensus objects (which are wait-free equivalent to k-set agreement objects in the read/write system model). This paper significantly extends the universality results introduced by Herlihy and Gafni-Guerraoui. In particular, we present a k-universal construction which satisfies the following five desired properties, which are not satisfied by the previous k-universal construction: (1) among the k objects that are constructed, at least $$\ell $$ objects (and not just one) are guaranteed to progress forever; (2) the progress condition for processes is wait-freedom, which means that each correct process executes an infinite number of operations on each object that progresses forever; (3) if any of the k constructed objects stops progressing, all its copies (one at each process) stop in the same state; (4) the proposed construction is contention-aware, in the sense that it uses only read/write registers in the absence of contention; and (5) it is generous with respect to the obstruction-freedom progress condition, which means that each process is able to complete any one of its pending operations on the k objects if all the other processes hold still long enough. The proposed construction, which is based on new design principles, is called a $$(k,\ell )$$ -universal construction. It uses a natural extension of k-simultaneous consensus objects, called $$(k,\ell )$$ -simultaneous consensus objects ( $$(k,\ell )$$ -SC). Together with atomic registers, $$(k,\ell )$$ -SC objects are shown to be necessary and sufficient for building a $$(k,\ell )$$ -universal construction, and, in that sense, $$(k,\ell )$$ -SC objects are $$(k,\ell )$$ - $$ {universal}$$ . [ABSTRACT FROM AUTHOR]
Published: 2016
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20. Anonymous obstruction-free (n, k)-set agreement with n-k+1 atomic read/write registers

Author: Bouzid, Zohir, Raynal, Michel, and Sutra, Pierre
Published: 2018
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21. Distributed computability: Relating k-immediate snapshot and x-set agreement.

Author: Delporte, Carole, Fauconnier, Hugues, Rajsbaum, Sergio, and Raynal, Michel
Abstract: This paper introduces a generalization of the immediate snapshot object denoted k-immediate snapshot, requiring that the snapshot returned contains at least (n − k) pairs. The case k = n − 1 corresponds to the original immediate snapshot object, which requires that the snapshot returned contains at least one pair 〈process id, value〉 pair, that corresponds to the process id that invoked the operation). The paper first shows that k -immediate snapshot is impossible to implement in an asynchronous read/write system, even if k = n − 2 and t = 1. Then, the paper considers x -set agreement, another object stronger than the classical read/write t -crash read/write model (when x ≤ t), and studies the relation with the k -immediate snapshot object, establishing strong relations linking these two fundamental distributed computing abstractions. The paper shows conditions under which x -set agreement can be solved in read/write systems enriched with k -immediate snapshot objects. It also shwos when k -immediate snapshot and consensus are equivalent. [ABSTRACT FROM AUTHOR]
Published: 2022
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22. Solving k-Set Agreement Using Failure Detectors in Unknown Dynamic Networks

Author: Pierre Sens, Thibault Rieutord, Luciana Arantes, Denis Jeanneau, Sens, Pierre, Large-Scale Distributed Systems and Applications (Regal), Laboratoire d'Informatique de Paris 6 (LIP6), Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Département Informatique et Réseaux (INFRES), Télécom ParisTech, Labex SMART, supported by French state funds managed by the ANR within the Investissements d’Avenir programmeunder reference ANR-11-LABX-65., and Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Discrete mathematics, 020203 distributed computing, K-set, Dynamic networks, Computer science, Detector, Failure detectors, k-Set agreement, 0102 computer and information sciences, 02 engineering and technology, Distributed systems, 01 natural sciences, Formalism (philosophy of mathematics), Computational Theory and Mathematics, 010201 computation theory & mathematics, Hardware and Architecture, Asynchronous communication, Signal Processing, [INFO.INFO-DC] Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], 0202 electrical engineering, electronic engineering, information engineering, Failure detector, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], Algorithm
Abstract: The failure detector abstraction has been used to solve agreement problems in asynchronous systems prone to crash failures, but so far it has mostly been used in static and complete networks. This paper aims to adapt existing failure detectors in order to solve agreement problems in unknown, dynamic systems. We are specifically interested in the k-set agreement problem. The problem of k-set agreement is a generalization of consensus where processes can decide up to k different values. Although some solutions to this problem have been proposed in dynamic networks, they rely on communication synchrony or make strong assumptions on the number of process failures. In this paper we consider unknown dynamic systems modeled using the formalism of Time-Varying Graphs, and extend the definition of the existing $\Pi \Sigma _{x,y}$ failure detector to obtain the $\Pi \Sigma _{\bot, x,y}$ failure detector, which is sufficient to solve k-set agreement in our model. We then provide an implementation of this new failure detector using connectivity and message pattern assumptions. Finally, we present an algorithm using $\Pi \Sigma _{\bot, x,y}$ to solve k-set agreement.
Published: 2017
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23. Failure Detectors in Dynamic Distributed Systems

Author: Jeanneau, Denis, DistributEd aLgorithms and sYStems (DELYS), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-LIP6, Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Sorbonne Université, Pierre Sens, and Luciana Arantes
Subjects: Consensus, K-Accord, Détecteurs de fautes, Systèmes distribués, Exclusion mutuelle, Mutual Exclusion, Failure detectors, Systèmes dynamiques, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], Distributed systems, Dynamic systems, K-set agreement
Abstract: Dynamic systems are distributed systems in which (1) processes can join or leave the system during the run, and (2) the communication graph evolves over time. The failure detector abstraction was introduced as a way to circumvent the impossibility of solving consensus in asynchronous systems prone to crash failures. A failure detector is a local oracle that provides processes in the system with unreliable information on process failures. But a failure detector that is sufficient to solve a given problem in a static system is not necessarily sufficient to solve the same problem in a dynamic system. Additionally, some existing failure detectors cannot be implemented in dynamic systems. Therefore, it is necessary to redefine existing failure detectors and provide new algorithms. In this thesis, we provide a new definition of a failure detector for k-set agreement, and prove that it is sufficient to solve k-set agreement in dynamic systems. We also design a dynamic system model and an algorithm that implements this new failure detector. Additionally, we adapt an existing failure detector for mutual exclusion and prove that it is still the weakest failure detector to solve mutual exclusion in dynamic systems, which means that it is weaker than any other failure detector capable of solving mutual exclusion.; Les systèmes dynamiques sont des systèmes distribués dans lesquels (1) les processus peuvent rejoindre ou quitter le système en cours d'exécution, et (2) le graphe de communication évolue au fil du temps. L'abstraction des détecteurs de fautes a été introduite afin de contourner l'impossibilité de résoudre le consensus dans les systèmes asynchrones sujets aux pannes franches. Mais un détecteur de fautes qui est suffisant pour résoudre un problème donné dans un système statique n'est pas nécessairement suffisant pour résoudre le même problème dans un système dynamique. Par conséquent, il est nécessaire de redéfinir les détecteurs de fautes existants et de concevoir de nouveaux algorithmes. Dans cette thèse, nous fournissons une nouvelle définition d'un détecteur de fautes pour le k-accord, et nous prouvons qu'il est suffisant pour résoudre le k-accord dans un système dynamique. Nous définissons également un modèle de système dynamique, ainsi qu'un algorithme capable d'implémenter ce nouveau détecteur de fautes dans notre modèle. De plus, nous adaptons un détecteur existant pour l'exclusion mutuelle et nous prouvons que même dans les systèmes dynamiques, il s'agit toujours du détecteur de fautes le plus faible pour résoudre l'exclusion mutuelle. Cela signifie que ce détecteur est plus faible que tous les autres détecteurs capables de résoudre l'exclusion mutuelle.
Published: 2018

24. Détecteurs de fautes pour les systèmes distribués dynamiques

Author: Jeanneau, Élise, DistributEd aLgorithms and sYStems (DELYS), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-LIP6, Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Sorbonne Université, Pierre Sens, and Luciana Arantes
Subjects: Consensus, K-Accord, Détecteurs de fautes, Systèmes distribués, Exclusion mutuelle, Failure detectors, Mutual Exclusion, Systèmes dynamiques, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], Distributed systems, Dynamic systems, K-set agreement
Abstract: Dynamic systems are distributed systems in which (1) processes can join or leave the system during the run, and (2) the communication graph evolves over time. The failure detector abstraction was introduced as a way to circumvent the impossibility of solving consensus in asynchronous systems prone to crash failures. A failure detector is a local oracle that provides processes in the system with unreliable information on process failures. But a failure detector that is sufficient to solve a given problem in a static system is not necessarily sufficient to solve the same problem in a dynamic system. Additionally, some existing failure detectors cannot be implemented in dynamic systems. Therefore, it is necessary to redefine existing failure detectors and provide new algorithms. In this thesis, we provide a new definition of a failure detector for k-set agreement, and prove that it is sufficient to solve k-set agreement in dynamic systems. We also design a dynamic system model and an algorithm that implements this new failure detector. Additionally, we adapt an existing failure detector for mutual exclusion and prove that it is still the weakest failure detector to solve mutual exclusion in dynamic systems, which means that it is weaker than any other failure detector capable of solving mutual exclusion.; Les systèmes dynamiques sont des systèmes distribués dans lesquels (1) les processus peuvent rejoindre ou quitter le système en cours d'exécution, et (2) le graphe de communication évolue au fil du temps. L'abstraction des détecteurs de fautes a été introduite afin de contourner l'impossibilité de résoudre le consensus dans les systèmes asynchrones sujets aux pannes franches. Mais un détecteur de fautes qui est suffisant pour résoudre un problème donné dans un système statique n'est pas nécessairement suffisant pour résoudre le même problème dans un système dynamique. Par conséquent, il est nécessaire de redéfinir les détecteurs de fautes existants et de concevoir de nouveaux algorithmes. Dans cette thèse, nous fournissons une nouvelle définition d'un détecteur de fautes pour le k-accord, et nous prouvons qu'il est suffisant pour résoudre le k-accord dans un système dynamique. Nous définissons également un modèle de système dynamique, ainsi qu'un algorithme capable d'implémenter ce nouveau détecteur de fautes dans notre modèle. De plus, nous adaptons un détecteur existant pour l'exclusion mutuelle et nous prouvons que même dans les systèmes dynamiques, il s'agit toujours du détecteur de fautes le plus faible pour résoudre l'exclusion mutuelle. Cela signifie que ce détecteur est plus faible que tous les autres détecteurs capables de résoudre l'exclusion mutuelle.
Published: 2018

25. k-Set Agreement and Renaming in the Presence of Contention-Related Crash Failures

Author: Michel Raynal, Gadi Taubenfeld, Anaïs Durand, the World Is Distributed Exploring the tension between scale and coordination (WIDE), Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-SYSTÈMES LARGE ÉCHELLE (IRISA-D1), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Rennes 1 (UR1), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), The Hong Kong Polytechnic University [Hong Kong] (POLYU), Interdisciplinay Center Herzliya - Israel (IDC), Interdisciplinay Center Herzliya, Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), and ANR-16-CE40-0023,DESCARTES,Abstraction modulaire pour le calcul distribué(2016)
Subjects: Correctness, Renaming, Concurrency, l-Mutual exclusion, Crash, 0102 computer and information sciences, k-Set agreement, Contention, Lambda, 01 natural sciences, Set (abstract data type), 03 medical and health sciences, 0302 clinical medicine, Atomic register, Asynchronous system, Impossibility, Agreement algorithm, Mathematics, Discrete mathematics, Read/write register, Process crash failure, 16. Peace & justice, 010201 computation theory & mathematics, Asynchronous communication, 030220 oncology & carcinogenesis, Participating process, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC]
Abstract: International audience; A new notion of process failure explicitly related to contention has recently been introduced by one of the authors (NETYS 2018). More precisely, given a predefined contention threshold λ, this notion considers the executions in which process crashes are restricted to occur only when process contention is smaller than or equal to λ. If crashes occur after contention bypassed λ, there are no correctness guarantees (e.g., termination is not guaranteed). It was shown that, when λ = n − 1, consensus can be solved in an n-process asynchronous read/write system despite the crash of one process, thereby circumventing the well-known FLP impossibility result. Furthermore, it was shown that when λ = n − k and k ≥ 2, k-set agreement can be solved despite the crash of 2k − 2 processes. This paper considers two types of process crash failures: "λ-constrained" crash failures (as previously defined), and classical crash failures (that we call "any time" failures). It presents two algorithms suited to these types of failures. The first algorithm solves k-set agreement, where k = m+f , in the presence of t = 2m + f − 1 crash failures, 2m of them being (n − k)-constrained failures, and (f − 1) being any time failures. The second algorithm solves (n + f)-renaming in the presence of t = m + f crash failures, m of them being (n − t − 1)-constrained failures, and f being any time failures. It follows that the differentiation between λ-constrained crash failures and any time crash failures enlarges the space of executions in which the impossibility of k-set agreement and renaming in the presence of asynchrony and process crashes can be circumvented. In addition to its behavioral properties, both algorithms have a noteworthy first class property, namely, their simplicity.
Published: 2018
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26. Anonymous obstruction-free (n,k)-set agreement with n−k+1 atomic read/write registers

Author: Bouzid, Zohir, Raynal, Michel, Sutra, Pierre, the World Is Distributed Exploring the tension between scale and coordination (WIDE), Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-SYSTÈMES LARGE ÉCHELLE (IRISA-D1), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Institut Universitaire de France (IUF), Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.), Département Informatique (TSP - INF), Institut Mines-Télécom [Paris] (IMT)-Télécom SudParis (TSP), Algorithmes, Composants, Modèles Et Services pour l'informatique répartie (ACMES-SAMOVAR), Services répartis, Architectures, MOdélisation, Validation, Administration des Réseaux (SAMOVAR), Institut Mines-Télécom [Paris] (IMT)-Télécom SudParis (TSP)-Institut Mines-Télécom [Paris] (IMT)-Télécom SudParis (TSP), Centre National de la Recherche Scientifique (CNRS), Université de Bretagne Sud (UBS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-CentraleSupélec-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Bretagne Sud (UBS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), and Département Informatique (INF)
Subjects: Consensus, Distributed algorithm, Colorless task, Atomic read/write register, Bounded num-ber of registers, Fault-tolerance, Distributed computability, Obstruction-freedom, Anonymous processes, Repeated k-set agreement, Asynchronous system, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], Process crash, Upper bound, K-set agreement
Abstract: International audience; The k-set agreement problem is a generalization of the consensus problem. Namely, assuming that each pro- cess proposes a value, every non-faulty process must decide one of the proposed values, under the constraint that at most k different values are decided. This is a hard problem in the sense that it cannot be solved in a pure read/write asyn- chronous system, in which k or more processes may crash. One way to sidestep this impossibility result consists in weak- ening the termination property, requiring only that a process decides if it executes alone during a long enough period of time. This is the well-known obstruction-freedom progress condition. Consider a system of n anonymous asynchronous processes that communicate through atomic read/write reg- isters, and such that any number of them may crash. This paper addresses and solves the challenging open problem of designing an obstruction-free k-set agreement algorithm with only (n −k +1) atomic registers. From a shared memory cost point of view, our algorithm is the best algorithm known to date, thereby establishing a new upper bound on the number of registers needed to solve this problem. For the consensus case (k = 1), the proposed algorithm is up to an additive factor of 1 close to the best known lower bound. Further, the paper extends this algorithm to obtain an x-obstruction- free solution to the k-set agreement problem that employs (n − k + x) atomic registers (with 1 ≤ x ≤ k < n), as well as a space-optimal solution for the repeated ver- sion of k-set agreement. Using this last extension, we prove that n registers are enough for every colorless task that is obstruction-free solvable with identifiers and any number of registers
Published: 2018
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27. t-Resilient Immediate Snapshot Is Impossible

Author: Carole Delporte, Sergio Rajsbaum, Hugues Fauconnier, Michel Raynal, Institut de Recherche en Informatique Fondamentale (IRIF (UMR_8243)), Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Networks, Graphs and Algorithms (GANG), Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), As Scalable As Possible: foundations of large scale dynamic distributed systems (ASAP), SYSTÈMES LARGE ÉCHELLE (IRISA-D1), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), CentraleSupélec-Télécom Bretagne-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Rennes (ENS Rennes)-Université de Bretagne Sud (UBS)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-CentraleSupélec-Télécom Bretagne-Université de Rennes 1 (UR1), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria), Instituto de Matematicas [México], Universidad Nacional Autónoma de México (UNAM), Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-SYSTÈMES LARGE ÉCHELLE (IRISA-D1), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Universidad Nacional Autónoma de México = National Autonomous University of Mexico (UNAM), Raynal, Michel, Institut Universitaire de France (IUF), Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.), Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Université de Bretagne Sud (UBS)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-CentraleSupélec-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Université de Rennes (UNIV-RENNES)-CentraleSupélec-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Université de Bretagne Sud (UBS)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Rennes (ENS Rennes)-Télécom Bretagne-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-CentraleSupélec, and DELPORTE-GALLET, CAROLE
Subjects: Theoretical computer science, Linearizability, Consensus, t-resilience, Computer science, Distributed computabil-ity, Crash, 0102 computer and information sciences, 02 engineering and technology, [INFO] Computer Science [cs], 01 natural sciences, Shared memory, Iterated model, 0202 electrical engineering, electronic engineering, information engineering, [INFO.INFO-DC] Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], [INFO]Computer Science [cs], Asynchronous system, Impossibility, Immediate snapshot, k-Set Agreement, Snapshot object, Process crash failure, 020207 software engineering, Atomic read/write register, ACM: F.: Theory of Computation, 010201 computation theory & mathematics, Wait-freedom, Snapshot (computer storage), Process identifier, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC]
Abstract: Immediate snapshot is the basic communication object on which relies the read/write distributed computing model made up of n crash-prone asynchronous processes, called iterated distributed model. Each iteration step (usually called a round) uses a new immediate snapshot object, which allows the processes to communicate and cooperate. More precisely, the x-th immediate snapshot object can be used by a process only when it executes the x-th round. An immediate snapshot object can be implemented by an (n − 1)-resilient algorithm, i.e. an algorithm that tolerates up to (n − 1) process crashes (also called wait-free algorithm). Considering a t-crash system model (i.e. a model in which up to t processes are allowed to crash), this paper is on the construction of an extension of immediate snapshot objects to t-resiliency. In the t-crash system model, at each round each process may be ensured to get values from at least n − t processes, and t-immediate snapshot has the properties of classical immediate snapshot (1-immediate snapshot) but ensures that each process will get values form at least n − t processes. Its main result is the following. While there is a (deterministic) t-resilient read/write-based algorithm implementing t-immediate snapshot in a t-crash system when t = n − 1, there is no t-resilient algorithm in a t-crash model when t ∈ [1..(n−2)]. This means that the notion of t-resilience is inop-erative when one has to implement immediate snapshot for these values of t: the model assumption " at most t < n − 1 processes may crash " does not provide us with additional computational power allowing for the design of genuine t-resilient algorithms (genuine meaning that such a t-resilient algorithm would work in the t-crash model, but not in the (t + 1)-crash model). To show these results, the paper relies on well-known distributed computing agreement problems such as consensus and k-set agreement.
Published: 2016

28. Modular randomized byzantine k-set agreement in asynchronous message-passing systems

Author: Hamouma Moumen, Michel Raynal, Achour Mostefaoui, Laboratoire des Sciences du Numérique de Nantes (LS2N), IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS), Gestion de Données Distribuées (GDD), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Université Mustapha Ben Boulaid de Batna 2, As Scalable As Possible: foundations of large scale dynamic distributed systems (ASAP), SYSTÈMES LARGE ÉCHELLE (IRISA-D1), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), CentraleSupélec-Télécom Bretagne-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Rennes (ENS Rennes)-Université de Bretagne Sud (UBS)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-CentraleSupélec-Télécom Bretagne-Université de Rennes 1 (UR1), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria), ANR-11-BS02-0014,DISPLEXITY,Calculabilité et complexité en distribué(2011), ANR-14-CE35-0010,DISCMAT,Mathematical Methods in Distributed Computing(2014), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Gestion de Données Distribuées (LS2N - équipe GDD), Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-SYSTÈMES LARGE ÉCHELLE (IRISA-D1), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), and Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)
Subjects: Randomized algorithm, Asynchronous system, Theoretical computer science, Byzantine process, Distributed algorithm, Computer science, Message passing, Coin, 0102 computer and information sciences, 02 engineering and technology, k-Set agreement, 01 natural sciences, Set (abstract data type), Asynchronous message-passing system, Quantum Byzantine agreement, 010201 computation theory & mathematics, Asynchronous communication, Broadcast abstraction, 0202 electrical engineering, electronic engineering, information engineering, Signature-free algorithm, 020201 artificial intelligence & image processing, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], Byzantine fault tolerance
Abstract: International audience; k-Set agreement is a central problem of fault-tolerant distibuted computing. Considering a set of n processes, where up to t may commit failures, let us assume that each process proposes a value. The problem consists in defining an algorithm such that each non-faulty process decides a value, at most k dfferent values are decided, and the decided values satisfy some context-depending validity condition. Synchronous message-passing algorithms solving k-set agreement have been proposed for different failure models (mainly process crashes, and process Byzantine failures). Differently, k-set agreement cannot be solved in failure-prone asynchronous message-passing systems when t ≥ k. To circumvent this impossibility an asynchronous system must be enriched with additional computational power. Assuming t ≥ k, this paper presents a distributed algorithm that solves k-set agreement in an asynchronous message-passing system wher up to t processes may commit Byzantine failures. To that end, each process is enriched with randomization power. While randomized k-set agreement algorithms exist for the asynchronous process crash failure model where t ≥ k, to our knowledge the proposed algorithm is the first that solves k-set agreement in the presence of up to t ≥ k Byzantine processes. Interestingly, this algorithm is signature-free, and ensures that no value proposed only by Byzantine processes can be decided by a non-faulty process. Its design is based on a modular construction which rests on a "no-duplicity" one-to-all broadcast abstraction, and two all-to-all communication abstractions.
Published: 2016

29. Anonymous Obstruction-free $(n,k)$-Set Agreement with $n-k+1$ Atomic Read/Write Registers

Author: Bouzid, Zohir, Raynal, Michel, Sutra, Pierre, As Scalable As Possible: foundations of large scale dynamic distributed systems (ASAP), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), SYSTÈMES LARGE ÉCHELLE (IRISA-D1), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria), Université de Neuchâtel (UNINE), univzrité de rennes 1, ASAP INRIA de Rennes, Université de Rennes (UR)-Inria Saclay - Ile de France, Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-SYSTÈMES LARGE ÉCHELLE (IRISA-D1), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), and Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)
Subjects: Consensus, Distributed algorithm, [INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS], Atomic read/write register, k-Set agreement, Bounded number of registers, Key-words: Anonymous processes, Fault-tolerance, Distributed computability, Obstruction-freedom, Repeated k-set agreement, Asynchronous system, Upper bound, Process crash
Abstract: The $k$-set agreement problem is a generalization of the consensus problem.Namely, assuming each process proposes a value, each non-faulty process has to decide a value such that each decided value was proposed, and no more than $k$ different values are decided. This is a hard problem in the sense thatit cannot be solved in asynchronous systems as soon as $k$ or more processes may crash. One way to circumvent this impossibility consists in weakening its termination property, requiring that a process terminates (decides) only if it executes alone during a long enough period. This is the well-known obstruction-freedom progress condition. Considering a system of $n$ {\it anonymous asynchronous} processes, which communicate through atomic {\it read/write registers only}, and where {\it any number of processes may crash}, this paper addresses and solves the challenging open problem of designing an obstruction-free $k$-set agreement algorithm with $(n-k+1)$ atomic registers only. From a shared memory cost point of view, this algorithm is the best algorithm known so far, thereby establishing a new upper bound on the numberof registers needed to solve the problem (its gain is $(n-k)$ with respect to the previous upper bound). The algorithm is then extended to address the repeated version of $(n,k)$-set agreement. As it is optimal in the number of atomic read/write registers, this algorithm closes the gap on previously established lower/upper boundsfor both the anonymous and non-anonymous versions of the repeated $(n,k)$-set agreement problem. Finally, for $1 \leq x\leq k < n$, a generalization suited to $x$-obstruction-freedom is also described, which requires $(n-k+x)$ atomic registers only.; Cet article préente un algorithme asynchrone qui résoud l'accord k-ensenbliste dans un système de n processus asynchrones et anonymes communiquant via $(n-k+1)$ registres atomiques du type lire/écrire, et dans lequel un nombre quelconque d'entre eux peut s'arrêterde façon inopinée (crash failure). La propriété de vivacité garantie par l'algorithme est appelée "obstruction-freedom".
Published: 2015

30. Strongly Terminating Early-Stopping k-Set Agreement in Synchronous Systems with General Omission Failures

Author: Raïpin Parvédy, Philippe, Raynal, Michel, and Travers, Corentin
Published: 2010
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31. Simultaneous Consensus vs Set Agreement: A Message-Passing-Sensitive Hierarchy of Agreement Problems

Author: Michel Raynal, Julien Stainer, As Scalable As Possible: foundations of large scale dynamic distributed systems (ASAP), Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-SYSTÈMES LARGE ÉCHELLE (IRISA-D1), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Institut Universitaire de France (IUF), Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.), ANR-11-BS02-0014,DISPLEXITY,Calculabilité et complexité en distribué(2011), SYSTÈMES LARGE ÉCHELLE (IRISA-D1), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Inria Rennes – Bretagne Atlantique, and Institut National de Recherche en Informatique et en Automatique (Inria)
Subjects: Class (set theory), Reduction (recursion theory), Simultaneous consensus, Liveness, Structure (category theory), k-Set agreement, 0102 computer and information sciences, 02 engineering and technology, 01 natural sciences, Set (abstract data type), Distributed computability, Consensus, 0202 electrical engineering, electronic engineering, information engineering, Asynchronous system, Reduction, Mathematics, Failure detector, Discrete mathematics, Hierarchy (mathematics), Fault tolerance, Distributed computing, Message-passing system, Shared memory, 010201 computation theory & mathematics, Wait-freedom, 020201 artificial intelligence & image processing, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], Quorum, Algorithm
Abstract: International audience; This paper investigates the relation linking the s-simultaneous consensus problem and the k-set agreement problem in wait-free message-passing systems. To this end, it first defines the (s,k)-SSA problem which captures jointly both problems: each process proposes a value, executes s simultaneous instances of a k-set agreement algorithm, and has to decide a value so that no more than sk different values are decided. The paper introduces then a new failure detector class denoted Z s,k , which is made up of two components, one focused on the "shared memory object" that allows the processes to cooperate, and the other focused on the liveness of (s,k)-SSA algorithms. A novelty of this failure detector lies in the fact that the definition of its two components are intimately related. Then, the paper presents a Z s,k -based algorithm that solves the (s,k)-SSA problem, and shows that the "shared memory"-oriented part of Z s,k is necessary to solve the (s,k)-SSA problem (this generalizes and refines a previous result that showed that the generalized quorum failure detector Σ k is necessary to solve k-set agreement). Finally, the paper investigates the structure of the family of (s,k)-SSA problems and introduces generalized (asymmetric) simultaneous set agreement problems in which the parameter k can differ in each underlying k-set agreement instance. Among other points, it shows that, for s,k > 1, (a) the (sk,1)-SSA problem is strictly stronger that the (s,k)-SSA problem which is itself strictly stronger than the (1,ks)-SSA problem, and (b) there are pairs (s 1,k 1) and (s 2,k 2) such that s 1 k 1 = s 2 k 2 and (s 1,k 1)-SSA and (s 2,k 2)-SSA are incomparable.; Cet article étudie les relations liant le problème du consensus s-simultané et celui de l'accord k-ensembliste.
Published: 2013
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32. Relations Linking Failure Detectors Associated with k-Set Agreement in Message-Passing Systems

Author: Michel Raynal, Julien Stainer, Achour Mostefaoui, As Scalable As Possible: foundations of large scale dynamic distributed systems (ASAP), Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-SYSTÈMES LARGE ÉCHELLE (IRISA-D1), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Xavier Défago et al., Rennes, Ist, SYSTÈMES LARGE ÉCHELLE (IRISA-D1), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria), and Mostefaoui, Achour
Subjects: Reduction (recursion theory), K-set, Computer science, [INFO.INFO-OH]Computer Science [cs]/Other [cs.OH], k-Set agreement, 0102 computer and information sciences, 02 engineering and technology, Topology, Equivalence, 01 natural sciences, Oracle, Distributed computability, [INFO.INFO-DC] Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], 0202 electrical engineering, electronic engineering, information engineering, Theory, Eventual leader, ComputingMilieux_MISCELLANEOUS, Reduction, Failure detector, 020203 distributed computing, Computability, Detector, Message passing, Fault tolerance, Impossibility, Asynchronous message-passing system, Fault-tolerance, [INFO.INFO-OH] Computer Science [cs]/Other [cs.OH], 010201 computation theory & mathematics, Asynchronous communication, Realistic failure detector, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], Quorum, Algorithm
Abstract: The k-set agreement problem is a coordination problem where each process is assumed to propose a value and each process that does not crash has to decide a value such that each decided value is a proposed value and at most k different values are decided. While it can always be solved in synchronous systems, k-set agreement has no solution in asynchronous send/receive message-passing systems where up to t ≥ k processes may crash. A failure detector is a distributed oracle that provides processes with additional information related to failed processes and can consequently be used to enrich the computability power of asynchronous send/receive message-passing systems. Several failure detectors have been proposed to circumvent the impossibility of k-set agreement in pure asynchronous send/receive message-passing systems. Considering three of them (namely, the generalized quorum failure detector ∑k, the generalized loneliness failure detector Lk and the generalized eventual leader failure detector k) the paper investigates their computability power and the relations that link them. It has three mains contributions: (a) it shows that the failure detector k and the eventual version of Lk have the same computational power; (b) it shows that Lk is realistic if and only if k ≽ n=2; and (c) it gives an exact characterization of the difference between Lk (that is too strong for k-set agreement) and Lk (that is too weak for k-set agreement)., Ce rapport reprend les différents détecteurs de fautes introduits pour renforcer les systèmes asynchrones et rendre le problème de k-accord décidable. En effet, plusieurs détecteurs de fautes ont été introduits mais certains sont trop forts et d'autres trop faibles. Ce rapport a pour but de déterminer l'espace qui sépare les premiers des seconds afin d'essayer de se rapprocher du détecteur minimal.
Published: 2011

33. Easy Impossibility Proofs for k-Set Agreement in Message Passing Systems

Author: Peter Robinson, Ulrich Schmid, Martin Biely, Fernandez Anta, Antonio, Lipari, Guiseppe, and Roy, Mathieu
Subjects: FOS: Computer and information sciences, Distributed Consensus, Theoretical computer science, K-set, Computer science, Proof of impossibility, 0102 computer and information sciences, 02 engineering and technology, Mathematical proof, k-set agreement, 01 natural sciences, Consensus, Lemma (logic), 0202 electrical engineering, electronic engineering, information engineering, C.2.4, Failure Detectors, Impossibility, Principle of bivalence, Discrete mathematics, 020203 distributed computing, Message passing, F.1.1, TheoryofComputation_GENERAL, 020207 software engineering, impossibility proofs, Shared memory, Computer Science - Distributed, Parallel, and Cluster Computing, consensus, 010201 computation theory & mathematics, Asynchronous communication, Distributed, Parallel, and Cluster Computing (cs.DC)
Abstract: Despite of being quite similar agreement problems, consensus and general k-set agreement require surprisingly different techniques for proving the impossibility in asynchronous systems with crash failures: Rather than relatively simple bivalence arguments as in the impossibility proof for consensus (= 1-set agreement) in the presence of a single crash failure, known proofs for the impossibility of k-set agreement in systems with at least k>1 crash failures use algebraic topology or a variant of Sperner's Lemma. In this paper, we present a generic theorem for proving the impossibility of k-set agreement in various message passing settings, which is based on a simple reduction to the consensus impossibility in a certain subsystem. We demonstrate the broad applicability of our result by exploring the possibility/impossibility border of k-set agreement in several message-passing system models: (i) asynchronous systems with crash failures, (ii) partially synchronous processes with (initial) crash failures, and (iii) asynchronous systems augmented with failure detectors. In (i) and (ii), the impossibility part is just an instantiation of our main theorem, whereas the possibility of achieving k-set agreement in (ii) follows by generalizing the consensus algorithm for initial crashes by Fisher, Lynch and Patterson. In (iii), applying our technique yields the exact border for the parameter k where k-set agreement is solvable with the failure detector class (Sigma_k,Omega_k), for (1, 15 pages
Published: 2011

34. Chasing the Weakest Failure Detector for k-Set Agreement in Message-passing Systems

Author: Achour Mostefaoui, Julien Stainer, Michel Raynal, Rennes, Ist, As Scalable As Possible: foundations of large scale dynamic distributed systems (ASAP), SYSTÈMES LARGE ÉCHELLE (IRISA-D1), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria), Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-SYSTÈMES LARGE ÉCHELLE (IRISA-D1), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Gestion de Données Distribuées [Nantes] (GDD), Laboratoire d'Informatique de Nantes Atlantique (LINA), Mines Nantes (Mines Nantes)-Université de Nantes (UN)-Centre National de la Recherche Scientifique (CNRS)-Mines Nantes (Mines Nantes)-Université de Nantes (UN)-Centre National de la Recherche Scientifique (CNRS), IUF, ANR Displexity, ANR-11-BS02-0014,DISPLEXITY,Calculabilité et complexité en distribué(2011), Centre National de la Recherche Scientifique (CNRS)-Mines Nantes (Mines Nantes)-Université de Nantes (UN)-Centre National de la Recherche Scientifique (CNRS)-Mines Nantes (Mines Nantes)-Université de Nantes (UN), CentraleSupélec-Télécom Bretagne-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Rennes (ENS Rennes)-Université de Bretagne Sud (UBS)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-CentraleSupélec-Télécom Bretagne-Université de Rennes 1 (UR1), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), and Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Inria Rennes – Bretagne Atlantique
Subjects: Reduction (recursion theory), K-set, Computer science, Distributed computing, [INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS], [INFO.INFO-OH]Computer Science [cs]/Other [cs.OH], 0102 computer and information sciences, 02 engineering and technology, k-Set agreement, 01 natural sciences, Electronic mail, Set (abstract data type), 0202 electrical engineering, electronic engineering, information engineering, Eventual leader, Set theory, Asynchronous system, Reduction, Discrete mathematics, Asynchronous distributed system, Failure detector, Wait-freedom, 020203 distributed computing, Message passing, Fault tolerance, Fault-tolerance, Message-passing system, [INFO.INFO-OH] Computer Science [cs]/Other [cs.OH], 010201 computation theory & mathematics, Asynchronous communication, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], Quorum
Abstract: This paper continues our quest for the weakest failure detector which allows the k-set agreement problem to be solved in asynchronous message-passing systems prone to any number of process failures. It has two main contributions which (we hope) will be instrumental to complete this quest. The first contribution is a new failure detector (denoted ∏∑x,y). This failure detector has several noteworthy properties. (a) It is stronger than ∑x which has been shown to be necessary. (b) It is equivalent to the pair (∑, Ω) when x = y = 1 (from which it follows that ∏∑1,1 is optimal to solve consensus). (c) It is equivalent to the pair (∑n−1, Ωn−1) when x = y = n − 1 (from which it follows that ∏∑n−1, n−1) is optimal for (n − 1)-set agreement). (d) It is strictly weaker than the pair (∑x,Ωy) (which has been investigated in previous works) for the pairs (x, y) such that 1 < y < x < n. (e) It is operational: the paper presents a ∏∑x,y-based algorithm that solves k-set agreement for k ⩾ xy. The second contribution of the paper is a proof that, for 1 < k < n − 1, the eventual leaders failure detector k (which eventually provides each process with the same set of k process identities, this set including at least one correct process) is not necessary to solve k-set agreement problem. More precisely, the paper shows that the weakest failure detector for k-set agreement and k cannot be compared.
Published: 2011
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35. Failure Detectors to Solve Asynchronous k-Set Agreement: a Glimpse of Recent Results

Author: Raynal, Michel, As Scalable As Possible: foundations of large scale dynamic distributed systems (ASAP), SYSTÈMES LARGE ÉCHELLE (IRISA-D1), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria), Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-SYSTÈMES LARGE ÉCHELLE (IRISA-D1), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), and Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)
Subjects: Failure detector, Wait-freedom, [INFO.INFO-OH]Computer Science [cs]/Other [cs.OH], Eventual leader, Message passing system, Asynchronous system, k-Set agreement, Shared memory system, Quorum
Abstract: In the k-set agreement problem, each process proposes a value and has to decide a value in such a way that a decided value is a proposed value and at most k different values are decided. This problem can easily be solved in synchronous systems or in asynchronous systems prone to t process crashes when t < k. In contrast, it has been shown that k-set agreement cannot be solved in asynchronous systems when k < t. Hence, since several years, the failure detector-based approach has been investigated to circumvent this impossibility. This approach consists in enriching the underlying asynchronous system with an additional module per process that provides it with information on failures. Hence, without becoming synchronous, the enriched system is no longer fully asynchronous. This paper surveys this approach in both asynchronous shared memory systems and asynchronous message passing systems. It presents and discusses recent results and associated k-set agreement algorithms.
Published: 2010

36. The Multiplicative Power of Consensus Numbers

Author: Damien Imbs, Michel Raynal, As Scalable As Possible: foundations of large scale dynamic distributed systems (ASAP), Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-SYSTÈMES LARGE ÉCHELLE (IRISA-D1), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), SYSTÈMES LARGE ÉCHELLE (IRISA-D1), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria), and Frey, Davide
Subjects: Reduction (recursion theory), ACM: C.: Computer Systems Organization/C.1: PROCESSOR ARCHITECTURES, Value (computer science), 0102 computer and information sciences, 02 engineering and technology, k-Set agreement, Shared memory system, 01 natural sciences, Upper and lower bounds, Consensus number, Synchronization power, Distributed computability, t-Resilience, System model, 0202 electrical engineering, electronic engineering, information engineering, ComputingMilieux_MISCELLANEOUS, Asynchronous processes, Mathematics, Discrete mathematics, Shared memory model, Fault-Tolerance, Multiplicative function, Process (computing), Waitfreedom, Process crash failure, 020207 software engineering, Base (topology), Power (physics), 010201 computation theory & mathematics, [INFO.INFO-OS]Computer Science [cs]/Operating Systems [cs.OS], BG simulation, Algorithm, Reduction algorithm
Abstract: The Borowsky-Gafni (BG) simulation algorithm is a powerful reduction algorithm that shows that t-resilience of decision tasks can be fully characterized in terms of wait-freedom. Said in another way, the BG simulation shows that the crucial parameter is not the number n of processes but the upper bound t on the number of processes that are allowed to crash. The BG algorithm considers colorless decision tasks in the base read/write shared memory model. (Colorless means that if, process decides a value, any other process is allowed to decide the very same value.) This paper considers system models made up of n processes prone to up to t crashes, and where the processes communicate by accessing read/write atomic registers (as assumed by the BG) and (differently from the BG) objects with consensus number x accessible by at most x processes (with x ≤ t n). Let ASM(n,t,x) denote such a system model. While the BG simulation has shown that the models ASM(n,t,1) and ASM(t+1,t,1) are equivalent, this paper focuses the pair (t,x) of parameters of a system model. Its main result is the following: the system models ASM (n1,t1,x1) and ASM (n2,t2,x2) have the same computational power for colorless decision tasks if and only if ⌊t1⁄x1⌋ = ⌊t1⁄x1⌋. As can be seen, this contribution complements and extends the BG simulation. It shows that consensus numbers have a multiplicative power with respect to failures, namely the system models ASM(n,t',x) and ASM(n,t,1) are equivalent for colorless decision tasks iff (t x x) ≤ t' ≤ (t x x)+(x-1).
Published: 2010

37. Synchronous Set Agreement: a Concise Guided Tour (with open problems)

Author: Raynal, Michel, Travers, Corentin, Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), and Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Round-based computation, Tolérance aux fautes, Consensus, Lower bound, Distributed algorithm, Agreement problem, Efficiency, Accord ensembliste, k-set agreement, ACM: D.: Software/D.4: OPERATING SYSTEMS/D.4.5: Reliability, ACM: C.: Computer Systems Organization/C.4: PERFORMANCE OF SYSTEMS, Early decision, Message-passing system, Crash failure, Omission en émission, Send omission failure, Synchronous system \\ Systèmes répartis asynchrones, Receive omission failure, Omission en réception, Crash de processus, [INFO.INFO-OS]Computer Science [cs]/Operating Systems [cs.OS], General omission failure
Abstract: The $k$-set agreement problem is a paradigm of coordination problems encountered in distributed computing. The parameter $k$ defines the coordination degree we are interested in. The case $k=1$ corresponds to the well-known uniform consensus problem. More precisely, the $k$-set agreement problem considers a system made up of $n$ processes where each process proposes a value. It requires that each non-faulty process decides a value such that a decided value is a proposed value, and no more than $k$ different values are decided. This paper visits the $k$-set agreement problem in synchronous systems where up to $t$ processes can experience failures. Three failure models are explored: the crash failure model, the send omission failure model, and the general omission failure model. Lower bounds and protocols are presented for each model. Open problems for the general omission failure model are stated. This paper can be seen as a short tutorial whose aim is to make the reader familiar with the $k$-set agreement problem in synchrony models with increasing fault severity. An important concern of the paper is simplicity. In addition to its survey flavor, several results and protocols that are presented are new. \\ Ce rapport constitue une visite guidé de l'accord ensembliste synchrone en présence de crashs, de fautes d'omission en émission, et de fautes d'omission en émission et réception.
Published: 2006

38. On the road to the weakest failure detector for k-set agreement in message-passing systems

Author: François Bonnet, Michel Raynal, As Scalable As Possible: foundations of large scale dynamic distributed systems (ASAP), SYSTÈMES LARGE ÉCHELLE (IRISA-D1), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), CentraleSupélec-Télécom Bretagne-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Rennes (ENS Rennes)-Université de Bretagne Sud (UBS)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-CentraleSupélec-Télécom Bretagne-Université de Rennes 1 (UR1), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria), Japan Advanced Institute of Science and Technology (JAIST), Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-SYSTÈMES LARGE ÉCHELLE (IRISA-D1), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), and Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)
Subjects: Class (set theory), Reduction (recursion theory), General Computer Science, K-set, Computer science, Structure (category theory), Asynchronous systems, Value (computer science), Quorums, 0102 computer and information sciences, 02 engineering and technology, Failure detectors, 01 natural sciences, k-set agreement, Theoretical Computer Science, Set (abstract data type), 0202 electrical engineering, electronic engineering, information engineering, ComputingMilieux_MISCELLANEOUS, Reduction, Discrete mathematics, Message passing, Eventual leaders, Shared memory, 010201 computation theory & mathematics, Message-passing systems, Wait-freedom, 020201 artificial intelligence & image processing, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], Algorithm
Abstract: In the k -set agreement problem, each process (in a set of n processes) proposes a value and has to decide a proposed value in such a way that at most k different values are decided. While this problem can easily be solved in asynchronous systems prone to t process crashes when k > t , it cannot be solved when k ≤ t . For several years, the failure-detector-based approach has been investigated to circumvent this impossibility. While the weakest failure detector class to solve the k -set agreement problem in read/write shared memory systems has recently been discovered (PODC 2009), the situation is different in message-passing systems where the weakest failure detector classes are known only for the extreme cases k = 1 (consensus) and k = n − 1 (set agreement). This paper presents four contributions whose aim is to help pave the way to discover the weakest failure detector class for k -set agreement in message-passing systems. These contributions are the following. (a) The first is a new failure detector class, denoted Π k , that is such that Π 1 = Σ × Ω (the weakest class for k = 1 ), and Π n − 1 = L (the weakest class for k = n − 1 ). (b) The second is an investigation of the structure of Π k that shows that Π k is the combination of two failure detector classes Σ k (that is new) and Ω k (they generalize the previous “quorums” and “eventual leaders” failure detector classes, respectively). (c) The third contribution concerns Σ k that is shown to be a necessary requirement (as far as information on failure is concerned) to solve the k -set agreement problem in message-passing systems. (d) Finally, the last contribution is a Π n − 1 -based algorithm that solves the ( n − 1 ) -set agreement problem. This algorithm provides us with a new algorithmic insight on the way the ( n − 1 ) -set agreement problem can be solved in asynchronous message-passing systems. It is hoped that these contributions will help discover the weakest failure detector class for k -set agreement in message-passing systems.
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