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Segment routing (SR) offers precise control over the paths taken: it specifies a list of detours, called segments, in IP packets. However, the number of detours that can be specified is limited by the hardware. When calculating segment lists, it is therefore necessary to limit their size. Although solutions have been proposed for calculating these lists, they lack generality and are not always optimal or efficient. We present ROUTOURNE, a method for diverting routing algorithms so that they calculate, not simply an optimal physical path to be translated into a list of segments a posteriori (with no guarantee of its size), but directly the optimal lists of segments deployable by the underlying hardware. ROUTOURNE thus facilitates the deployment of advanced traffic engineering strategies and policies, notably for load balancing from sources. Despite a route fraught with surprising challenges - in particular, the loss of isotonicity induced by SR - ROUTOURNE proves efficient, inducing at worst a linear overhead. Its accuracy and optimality have been proven, and its effectiveness evaluated by generalizing it to several more or less complex path calculation algorithms., Comment: in French language. AlgoTel 2024 -- 26{\`e}mes Rencontres Francophones sur les Aspects Algorithmiques des T{\'e}l{\'e}communications, May 2024, Saint-Briac-sur-Mer, France

We consider a collection of $k \geq 2$ robots that evolve in a ring-shaped network without common orientation, and address a variant of the crash-tolerant gathering problem called the \emph{Stand-Up Indulgent Gathering} (SUIG): given a collection of robots, if no robot crashes, robots have to meet at the same arbitrary location, not known beforehand, in finite time; if one robot or more robots crash on the same location, the remaining correct robots gather at the location of the crashed robots. We aim at characterizing the solvability of the SUIG problem without multiplicity detection capability.

We consider a strong variant of the crash fault-tolerant gathering problem called stand-up indulgent gathering (SUIG), by robots endowed with limited visibility sensors and lights on line-shaped networks. In this problem, a group of mobile robots must eventually gather at a single location, not known beforehand, regardless of the occurrence of crashes. Differently from previous work that considered unlimited visibility, we assume that robots can observe nodes only within a certain fixed distance (that is, they are myopic), and emit a visible color from a fixed set (that is, they are luminous), without multiplicity detection. We consider algorithms depending on two parameters related to the initial configuration: $M_{init}$, which denotes the number of nodes between two border nodes, and $O_{init}$, which denotes the number of nodes hosting robots. Then, a border node is a node hosting one or more robots that cannot see other robots on at least one side. Our main contribution is to prove that, if $M_{init}$ or $O_{init}$ is odd, SUIG can be solved in the fully synchronous model.

We consider a variant of the crash-fault gathering problem called stand-up indulgent gathering (SUIG). In this problem, a group of mobile robots must eventually gather at a single location, which is not known in advance. If no robots crash, they must all meet at the same location. However, if one or more robots crash at a single location, all non-crashed robots must eventually gather at that location. The SUIG problem was first introduced for robots operating in a two-dimensional continuous Euclidean space, with most solutions relying on the ability of robots to move a prescribed (real) distance at each time instant. In this paper, we investigate the SUIG problem for robots operating in a discrete universe (i.e., a graph) where they can only move one unit of distance (i.e., to an adjacent node) at each time instant. Specifically, we focus on line-shaped networks and characterize the solvability of the SUIG problem for oblivious robots without multiplicity detection.

We consider a swarm of mobile robots evolving in a bidimensional Euclidean space. We study a variant of the crash-tolerant gathering problem: if no robot crashes, robots have to meet at the same arbitrary location, not known beforehand, in finite time; if one or several robots crash at the same location, the remaining correct robots gather at the crash location to rescue them. Motivated by impossibility results in the semi-synchronous setting, we present the first solution to the problem for the fully synchronous setting that operates in the vanilla Look-Compute-Move model with no additional hypotheses: robots are oblivious, disoriented, have no multiplicity detection capacity, and may start from arbitrary positions (including those with multiplicity points). We furthermore show that robots gather in a time that is proportional to the initial maximum distance between robots., Comment: arXiv admin note: substantial text overlap with arXiv:2010.04400

We consider transportation networks that are modeled by dynamic graphs, and introduce the possibility for traveling agents to use Backward Time-Travel (BTT) devices at any node to go back in time (to some extent, and with some appropriate fee) before resuming their trip. We focus on dynamic line graphs. In more detail, we propose exact algorithms to compute travel plans with constraints on the BTT cost or on how far back in time you can go, while minimizing travel delay (that is, the time difference between the arrival instant and the starting instant), in polynomial time. We study the impact of the BTT devices pricing policies on the computation process of those plans considering travel delay and cost, and provide necessary properties that pricing policies should satisfy to enable to compute such plans. Finally, we provide an optimal online algorithm for the unconstrained problem when the cost function is the identity.

The Tangle is the data structure used to store transactions in the IOTA cryptocurrency. In the Tangle, each block has two parents. As a result, the blocks do not form a chain, but a directed acyclic graph. In traditional Blockchain, a new block is appended to the heaviest chain in case of fork. In the Tangle, the parent selection is done by the Tip Selection Algorithm (TSA). In this paper, we make some important observations about the security of existing TSAs. We then propose a new TSA that has low complexity and is more secure than previous TSAs.

With a growing demand for quasi-instantaneous communication services such as real-time video streaming, cloud gaming, and industry 4.0 applications, multi-constraint Traffic Engineering (TE) becomes increasingly important. While legacy TE management planes have proven laborious to deploy, Segment Routing (SR) drastically eases the deployment of TE paths and is thus increasingly adopted by Internet Service Providers (ISP). There is a clear need in computing and deploying Delay-Constrained Least-Cost paths (DCLC) with SR for real-time interactive services. However, most current DCLC solutions are not tailored for SR. They also often lack efficiency or guarantees. Similarly to approximation schemes, we argue that the challenge is to design an algorithm providing both performances and guarantees. However, conversely to most of these schemes, we also consider operational constraints to provide a practical, high-performance implementation. We leverage the inherent limitations of delay measurements and account for the operational constraint added by SR to design a new algorithm, best2cop, providing guarantees and performance in all cases. Best2cop outperforms a state-of-the-art algorithm on both random and real networks of up to 1000 nodes. Relying on commodity hardware with a single thread, our algorithm retrieves all non-superfluous 3-dimensional routes in only 250ms and 100ms respectively. This execution time is further reduced using multiple threads, as the design of best2cop enables a speedup almost linear in the number of cores. Finally, we extend best2cop to deal with massive scale ISP by leveraging the multi-area partitioning of these deployments. Thanks to our new topology generator specifically designed to model the realistic patterns of such massive IP networks, we show that best2cop solves DCLC-SR in approximately 1 second even for ISP having more than 100000 routers.

Interactions between the intra- and inter-domain routing protocols received little attention despite playing an important role in forwarding transit traffic. More precisely, by default, IGP distances are taken into account by BGP to select the closest exit gateway for the transit traffic (hot-potato routing). Upon an IGP update, the new best gateway may change and should be updated through the (full) re-convergence of BGP, causing superfluous BGP processing and updates in many cases. We propose OPTIC (Optimal Protection Technique for Inter-intra domain Convergence), an efficient way to assemble both protocols without losing the hot-potato property. OPTIC pre-computes sets of gateways (BGP next-hops) shared by groups of prefixes. Such sets are guaranteed to contain the post-convergence gateway after any single IGP event for the grouped prefixes. The new optimal exits can be found through a single walk-through of each set, allowing the transit traffic to benefit from optimal BGP routes almost as soon as the IGP converges. Compared to vanilla BGP, OPTIC's structures allow it to consider a reduced number of entries: this number can be reduced by 99\% for stub networks. The update of OPTIC's structures, which is not required as long as border routers remain at least bi-connected, scales linearly in time with its number of groups., Comment: IEEE INFOCOM 2021, May 2021, Online, France

With the growth of demands for quasi-instantaneous communication services such as real-time video streaming, cloud gaming, and industry 4.0 applications, multi-constraint Traffic Engineering (TE) becomes increasingly important. While legacy TE management planes have proven laborious to deploy, Segment Routing (SR) drastically eases the deployment of TE paths and thus became the most appropriate technology for many operators. The flexibility of SR sparked demands in ways to compute more elaborate paths. In particular, there exists a clear need in computing and deploying Delay-Constrained Least-Cost paths (DCLC) for real-time applications requiring both low delay and high bandwidth routes. However, most current DCLC solutions are heuristics not specifically tailored for SR. In this work, we leverage both inherent limitations in the accuracy of delay measurements and an operational constraint added by SR. We include these characteristics in the design of BEST2COP, an exact but efficient ECMP-aware algorithm that natively solves DCLC in SR domains. Through an extensive performance evaluation, we first show that BEST2COP scales well even in large random networks. In real networks having up to thousands of destinations, our algorithm returns all DCLC solutions encoded as SR paths in way less than a second.

We consider two mobile oblivious robots that evolve in a continuous Euclidean space. We require the two robots to solve the rendezvous problem (meeting in finite time at the same location, not known beforehand) despite the possibility that one of those robots crashes unpredictably. The rendezvous is stand up indulgent in the sense that when a crash occurs, the correct robot must still meet the crashed robot on its last position. We characterize the system assumptions that enable problem solvability, and present a series of algorithms that solve the problem for the possible cases.

In public distributed ledger technologies (DLTs), such as Blockchains, nodes can join and leave the network at any time. A major challenge occurs when a new node joining the network wants to retrieve the current state of the ledger. Indeed, that node may receive conflicting information from honest and Byzantine nodes, making it difficult to identify the current state. In this paper, we are interested in protocols that are stateless, i.e., a new joining node should be able to retrieve the current state of the ledger just using a fixed amount of data that characterizes the ledger (such as the genesis block in Bitcoin). We define three variants of stateless DLTs: weak, strong, and probabilistic. Then, we analyze this property for DLTs using different types of consensus.

In this paper, we present several improvements in the parallelization of the in-place merge algorithm, which merges two contiguous sorted arrays into one with an O(T) space complexity (where T is the number of threads). The approach divides the two arrays into as many pairs of partitions as there are threads available; such that each thread can later merge a pair of partitions independently of the others. We extend the existing method by proposing a new algorithm to find the median of two partitions. Additionally, we provide a new strategy to divide the input arrays where we minimize the data movement, but at the cost of making this stage sequential. Finally, we provide the so-called linear shifting algorithm that swaps two partitions in-place with contiguous data access. We emphasize that our approach is straightforward to implement and that it can also be used for external (out of place) merging. The results demonstrate that it provides a significant speedup compared to sequential executions, when the size of the arrays is greater than a thousand elements.

This paper we define a new Puzzle called Proof-of-Interaction and we show how it can replace, in the Bitcoin protocol, the Proof-of-Work algorithm.

We deal with a set of autonomous robots moving on an infinite grid. Those robots are opaque, have limited visibility capabilities, and run using synchronous Look-Compute-Move cycles. They all agree on a common chirality, but have no global compass. Finally, they may use lights of different colors, but except from that, robots have neither persistent memories, nor communication mean. We consider the infinite grid exploration (IGE) problem. For this problem we give two impossibility results and three algorithms, including one which is optimal in terms of number of robots. In more detail, we first show that two robots are not sufficient in our settings to solve the problem, even when robots have a common coordinate system. We then show that if the robots' coordinate systems are not self-consistent, three or four robots are not sufficient to solve the problem. Finally, we present three algorithms that solve the IGE problem in various settings. The first algorithm uses six robots with constant colors and a visibility range of one. The second one uses the minimum number of robots, i.e., five, as well as five modifiable colors, still under visibility one. The last algorithm requires seven oblivious anonymous robots, yet assuming visibility two. Notice that the two last algorithms also satisfy achieve exclusiveness., Comment: 22 pages

We consider the problem of aggregating data in a dynamic graph, that is, aggregating the data that originates from all nodes in the graph to a specific node, the sink. We are interested in giving lower bounds for this problem, under different kinds of adversaries. In our model, nodes are endowed with unlimited memory and unlimited computational power. Yet, we assume that communications between nodes are carried out with pairwise interactions, where nodes can exchange control information before deciding whether they transmit their data or not, given that each node is allowed to transmit its data at most once. When a node receives a data from a neighbor, the node may aggregate it with its own data. We consider three possible adversaries: the online adaptive adversary, the oblivious adversary , and the randomized adversary that chooses the pairwise interactions uniformly at random. For the online adaptive and the oblivious adversary, we give impossibility results when nodes have no knowledge about the graph and are not aware of the future. Also, we give several tight bounds depending on the knowledge (be it topology related or time related) of the nodes. For the randomized adversary, we show that the Gathering algorithm, which always commands a node to transmit, is optimal if nodes have no knowledge at all. Also, we propose an algorithm called Waiting Greedy, where a node either waits or transmits depending on some parameter, that is optimal when each node knows its future pairwise interactions with the sink.

We propose a new probabilistic pattern formation algorithm for oblivious mobile robots that operates inthe ASYNC model. Unlike previous work, our algorithm makes no assumptions about the local coordinatesystems of robots (the robots do not share a common "North" nor a common "Right"), yet it preserves theability from any initial configuration that contains at least 5 robots to form any general pattern (and not justpatterns that satisfy symmetricity predicates). Our proposal also gets rid of the previous assumption (in thesame model) that robots do not pause while moving (so, our robots really are fully asynchronous), and theamount of randomness is kept low -- a single random bit per robot per Look-Compute-Move cycle is used.Our protocol consists in the combination of two phases, a probabilistic leader election phase, and a deterministicpattern formation one. As the deterministic phase does not use chirality, it may be of independentinterest in the deterministic context. A noteworthy feature of our algorithm is the ability to form patternswith multiplicity points (except the gathering case due to impossibility results), a new feature in the contextof pattern formation that we believe is an important asset of our approach.

We assume that a message may be delivered by packets through multiple hops and investigate the feasibility and efficiency of an implementation of the Omega Failure Detector under such an assumption.To motivate the study, we prove that the existence and sustainability of a leader is exponentially more probable in a multi-hop Omega implementation than in a single-hop one.An implementation is: \emph{message efficient} if all but finitely many messages are sent by a single process; \emph{packet efficient} if the number of packets used to transmit a message in all but finitely many messages is linear w.r.t the number of processes, packets of different messages may potentially use different channels, thus the number of used channels is not limited; \emph{super packet efficient} if the number of channels used by packets to transmit all but finitely many messages is linear.We present the following results for deterministic algorithms. If reliability and timeliness of one message does not correlate with another, i.e., there are no channel reliability properties, then a packet efficient implementation of Omega is impossible. If eventuallytimely and fair-lossy channels are considered, we establish necessary and sufficient conditions for the existence of a message and packet efficient implementation of Omega. We also prove that the eventuality of timeliness of channels makes a super packet efficientimplementation of Omega impossible. On the constructive side, we present and prove correct a deterministic packet efficient implementation of Omega that matches the necessary conditions we established.

We consider the problem of scattering $n$ robots in a two dimensional continuous space. As this problem is impossible to solve in a deterministic manner, all solutions must be probabilistic. We investigate the amount of randomness (that is, the number of random bits used by the robots) that is required to achieve scattering. We first prove that $n \log n$ random bits are necessary to scatter $n$ robots in any setting. Also, we give a sufficient condition for a scattering algorithm to be random bit optimal. As it turns out that previous solutions for scattering satisfy our condition, they are hence proved random bit optimal for the scattering problem. Then, we investigate the time complexity of scattering when strong multiplicity detection is not available. We prove that such algorithms cannot converge in constant time in the general case and in $o(\log \log n)$ rounds for random bits optimal scattering algorithms. However, we present a family of scattering algorithms that converge as fast as needed without using multiplicity detection. Also, we put forward a specific protocol of this family that is random bit optimal ($n \log n$ random bits are used) and time optimal ($\log \log n$ rounds are used). This improves the time complexity of previous results in the same setting by a $\log n$ factor. Aside from characterizing the random bit complexity of mobile robot scattering, our study also closes its time complexity gap with and without strong multiplicity detection (that is, $O(1)$ time complexity is only achievable when strong multiplicity detection is available, and it is possible to approach it as needed otherwise).