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This paper introduces the RoboCast communication abstraction. The RoboCast allows a swarm of non oblivious, anonymous robots that are only endowed with visibility sensors and do not share a common coordinate system, to asynchronously exchange information. We propose a generic framework that covers a large class of asynchronous communication algorithms and show how our framework can be used to implement fundamental building blocks in robot networks such as gathering or stigmergy. In more details, we propose a RoboCast algorithm that allows robots to broadcast their local coordinate systems to each others. Our algorithm is further refined with a local collision avoidance scheme. Then, using the RoboCast primitive, we propose algorithms for deterministic asynchronous gathering and binary information exchange. [ABSTRACT FROM AUTHOR]

We explore asynchronous unison in the presence of systemic transient and permanent Byzantine faults in shared memory. We observe that the problem is not solvable under less than strongly fair scheduler or for system topologies with maximum node degree greater than two. We present a self-stabilizing Byzantine-tolerant solution to asynchronous unison for chain and ring topologies. Our algorithm has minimum possible containment radius and optimal stabilization time. [ABSTRACT FROM AUTHOR]

Self-stabilization guarantees convergence to a legitimate configuration in every execution starting from any initial configuration. However, during convergence, most self-stabilizing protocols make unnecessary output changes that do not directly contribute to the progress of convergence. We define and study monotonic stabilization, where every output change is a step toward convergence. That is, any output change at a process p gives the final output of p in the legitimate configuration to be reached. It turns out that monotonic stabilization requires additional information exchange between processes, and we present task dependent tradeoff results with respect to the locality of exchanged information. [ABSTRACT FROM AUTHOR]

The maximum leaf spanning tree (MLST) is a good candidate for constructing a virtual backbone in self-organized multihop wireless networks, but is practically intractable (NP-complete). Self-stabilization is a general technique that permits to recover from catastrophic transient failures in self-organized networks without human intervention. We propose a fully distributed self-stabilizing approximation algorithm for the MLST problem on arbitrary topology networks. Our algorithm is the first self-stabilizing protocol that is specifically designed for the construction of an MLST. It improves other previous self-stabilizing solutions both for generality (arbitrary topology graphs vs. unit disk graphs or generalized disk graphs, respectively) and for approximation ratio, as it guarantees the number of its leaves is at least 1/3 of the maximum one. The time complexity of our algorithm is O(n2) rounds. [ABSTRACT FROM AUTHOR]

We consider the problem of exploring an anonymous unoriented ring of size n by k identical, oblivious, asynchronous mobile robots, that are unable to communicate, yet have the ability to sense their environment and take decisions based on their local view. Previous works in this weak scenario prove that k must not divide n for a deterministic solution to exist. Also, it is known that the minimum number of robots (either deterministic or probabilistic) to explore a ring of size n is 4. An upper bound of 17 robots holds in the deterministic case while 4 probabilistic robots are sufficient. In this paper, we close the complexity gap in the deterministic setting, by proving that no deterministic exploration is feasible with less than five robots, and that five robots are sufficient for any n that is coprime with five. Our protocol completes exploration in O(n) robot moves, which is also optimal. [ABSTRACT FROM AUTHOR]

We consider a team of k identical, oblivious, semi-synchronous mobile robots that are able to sense (i.e., view) their environment, yet are unable to communicate, and evolve on a constrained path. Previous results in this weak scenario show that initial symmetry yields high lower bounds when problems are to be solved by deterministic robots. In this paper, we initiate research on probabilistic bounds and solutions in this context, and focus on the exploration problem of anonymous unoriented rings of any size. It is known that Θ(logn) robots are necessary and sufficient to solve the problem with k deterministic robots, provided that k and n are coprime. By contrast, we show that four identical probabilistic robots are necessary and sufficient to solve the same problem, also removing the coprime constraint. Our positive results are constructive. [ABSTRACT FROM AUTHOR]

A distributed algorithm is self-stabilizing if after faults and attacks hit the system and place it in some arbitrary global state, the system recovers from this catastrophic situation without external intervention in finite time. Unidirectional networks preclude many common techniques in self-stabilization from being used, such as preserving local predicates. The focus of this work is on the classical vertex coloring problem, that is a basic building block for many resource allocation problems arising in wireless sensor networks. In this paper, we investigate the gain in complexity that can be obtained through randomization. We present a probabilistically self- stabilizing algorithm that uses k states per process, where k is a parameter of the algorithm. When k = ∆ + 1, the algorithm recovers in expected O(∆n) actions. When k may grow arbitrarily, the algorithm recovers in expected O(n) actions in total. Thus, our algorithm can be made optimal with respect to space or time complexity. Our case study hints that randomization could help filling the complexity gap between bidirectionnal and unidirectionnal networks. [ABSTRACT FROM AUTHOR]

We propose an univesal scheme to design loop-free and super-stabilizing protocols for constructing spanning trees optimizing any tree metrics (not only those that are isomorphic to a shortest path tree). Our scheme combines a novel super-stabilizing loop-free BFS with an existing self-stabilizing spanning tree that optimizes a given metric. The composition result preserves the best properties of both worlds: super-stabilization, loop-freedom, and optimization of the original metric without any stabilization time penalty. As case study we apply our composition mechanism to two well known metric-dependent spanning trees: the maximum-flow tree and the minimum degree spanning tree. [ABSTRACT FROM AUTHOR]

Self-stabilization is a versatile approach to fault-tolerance since it permits a distributed system to recover from any transient fault that arbitrarily corrupts the contents of all memories in the system. Byzantine tolerance is an attractive feature of distributed systems that permits to cope with arbitrary malicious behaviors. We consider the well known problem of constructing a breadth-first spanning tree in this context. Combining these two properties prove difficult: we demonstrate that it is impossible to contain the impact of Byzantine processes in a strictly or strongly stabilizing manner. We then adopt the weaker scheme of topology-aware strict stabilization and we present a similar weakening of strong stabilization. We prove that the classical min + 1 protocol has optimal Byzantine containment properties with respect to these criteria. [ABSTRACT FROM AUTHOR]

The scattering problem is a fundamental task for mobile robots, which requires that no two robots share the same position. We investigate the scattering problem in the limited-visibility model. In particular, we focus on connectivity-preservation property. That is, the scattering must be achieved so that the disconnection of the visibility graph never occurs (in the visibility graph robots are the nodes of the graph and the edges are their visibility relationship). The algorithm we propose assumes ATOM (i.e. semi-synchronous) model. In these settings our algorithm guarantees the connectivity-preserving property, and reaches a scattered configuration within O( min {n, D2 + logn}) asynchronous rounds in expectation, where D is the diameter of the initial visibility graph. Note that the complexity analysis is adaptive since it depends on D. This implies that our algorithm quickly scatters all robots crowded in a small-diameter visibility graph. We also provide a lower bound of Ώ(n) for connectivity-preserving scattering. It follows that our algorithm is optimal in the sense of the non-adaptive analysis. [ABSTRACT FROM AUTHOR]

We propose a novel and totally decentralized strategy for private and secure data exchange in peer-to-peer systems. Our scheme is particularly appealing for point-to-point exchanges and use zero-knowledge mechanisms to preserve privacy. Furthermore, we show how to plug our private and secure data exchange module in existing publish/subscribe architectures. Our proposal enriches the original system with security and privacy making it resilient to a broad class of attacks (e.g. brute-force, eavesdroppers, man-in-the middle or malicious insiders). Additionally, the original properties of the publish/subscribe system are preserved without any degradation. A nice feature of our proposal is the reduce message cost: only one extra message is sent for every message sent in the original system. Note that our contribution is more conceptual than experimental and can be easily exploited by new emergent areas such as P2P Internet Games or Social Networks where a major trend is to achieve a secure and private communication without relying on any fixed infrastructure or centralized authority. [ABSTRACT FROM AUTHOR]

In this paper, we study the exclusive perpetual exploration problem with mobile anonymous and oblivious robots in a discrete space. Our results hold for the most generic settings: robots are asynchronous and are not given any sense of direction, so the left and right sense (i.e. chirality) is decided by the adversary that schedules robots for execution, and may change between invocations of a particular robots (as robots are oblivious). We investigate both the minimal and the maximal number of robots that are necessary and sufficient to solve the exclusive perpetual exploration problem. On the minimal side, we prove that three deterministic robots are necessary and sufficient, provided that the size n of the ring is at least 10, and show that no protocol with three robots can exclusively perpetually explore a ring of size less than 10. On the maximal side, we prove that k = n − 5 robots are necessary and sufficient to exclusively perpetually explore a ring of size n when n is co-prime with k. [ABSTRACT FROM AUTHOR]

Self-stabilization is a versatile approach to fault-tolerance since it permits a distributed system to recover from any transient fault that arbitrarily corrupts the contents of all memories in the system. Byzantine tolerance is an attractive feature of distributed systems that permits to cope with arbitrary malicious behaviors. We consider the well known problem of constructing a maximum metric tree in this context. Combining these two properties proves difficult: we demonstrate that it is impossible to contain the impact of Byzantine nodes in a self-stabilizing context for maximum metric tree construction (strict stabilization). We propose a weaker containment scheme called topology-aware strict stabilization, and present a protocol for computing maximum metric trees that is optimal for this scheme with respect to impossibility result. [ABSTRACT FROM AUTHOR]

This paper addresses the byzantine resilience lower bound for the convergence in semi-synchronous robot networks. We prove that 3f + 1 robots are needed for convergence to tolerate up to f Byzantine robots. Our work generalizes the previously established lower bound proved for the class of cautious algorithms only. Additionally we propose the first deterministic algorithm that matches this lower bound and performs in the asynchronous CORDA model. Our algorithm works under bounded scheduling assumptions for oblivious robots moving in a uni-dimensional space. [ABSTRACT FROM AUTHOR]

The minimum spanning tree (MST) construction is a classical problem in Distributed Computing for creating a globally minimized structure distributedly. Self-stabilization is versatile technique for forward recovery that permits to handle any kind of transient faults in a unified manner. The loop-free property provides interesting safety assurance in dynamic networks where edge-cost changes during operation of the protocol. We present a new self-stabilizing MST protocol that improves on previous known approaches in several ways. First, it makes fewer system hypotheses as the size of the network (or an upper bound on the size) need not be known to the participants. Second, it is loop-free in the sense that it guarantees that a spanning tree structure is always preserved while edge costs change dynamically and the protocol adjusts to a new MST. Finally, time complexity matches the best known results, while space complexity results show that this protocol is the most efficient to date. [ABSTRACT FROM AUTHOR]

We consider snap-stabilization in message-passing systems. Snap-stabilization permits to design protocols that withstand transient faults: Any computation that is started after faults cease immediately satisfies the expected specification. Our contribution is twofold, as we demonstrate that in message passing systems (i) snap-stabilization is impossible for nontrivial problems if we consider channels with finite yet unbounded capacity, and (ii) snap-stabilization becomes possible in the same setting with bounded-capacity channels. The latter contribution is constructive, as we propose two snap-stabilizing protocols. [ABSTRACT FROM AUTHOR]

Given a set of robots with arbitrary initial location and no agreement on a global coordinate system, convergence requires that all robots asymptotically approach the exact same, but unknown beforehand, location. Robots are oblivious– they do not recall the past computations – and are allowed to move in a one-dimensional space. Additionally, robots cannot communicate directly, instead they obtain system related information only via visual sensors. We prove ([4]) necessary and sufficient conditions for the convergence of mobile robots despite a subset of them being Byzantine (i.e. they can exhibit arbitrary behavior). Additionally, we propose a deterministic convergence algorithm for robot networks and analyze its correctness and complexity in various synchrony settings. The proposed algorithm tolerates f Byzantine robots for (2f + 1)-sized robot networks in fully synchronous networks, (3f + 1)-sized in semi-synchronous networks and (4f + 1)-sized in asynchronous networks. The bounds obtained for the ATOM model are optimal for the class of cautious algorithms, which guarantee that correct robots always move inside the range of positions of the correct robots. [ABSTRACT FROM AUTHOR]