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

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 that it 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 number of 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 bounds for both the anonymous and non-anonymous versions of the repeated $(n,k)$-set agreement problem. Finally, for 1 \leq x\leq k \textless{} n, a generalization suited to $x$-obstruction-freedom is also described, which requires $(n-k+x)$ atomic registers only

Optimal byzantine resilient convergence in oblivious robot networks

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 draw a connection between the convergence problem in robot networks, and the distributed \emph{approximate agreement} problem (that requires correct processes to decide, for some constant $\epsilon$, values distance $\epsilon$ apart and within the range of initial proposed values). Surprisingly, even though specifications are similar, the convergence implementation in robot networks requires specific assumptions about synchrony and Byzantine resilience. In more details, we prove 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. These bounds are optimal for the class of cautious algorithms, which guarantee that correct robots always move inside the range of positions of the correct robots

RoboCast: Asynchronous Communication in Robot Networks

This paper introduces the \emph{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

Certified Impossibility Results for Byzantine-Tolerant Mobile Robots

We propose a framework to build formal developments for robot networks using the COQ proof assistant, to state and to prove formally various properties. We focus in this paper on impossibility proofs, as it is natural to take advantage of the COQ higher order calculus to reason about algorithms as abstract objects. We present in particular formal proofs of two impossibility results forconvergence of oblivious mobile robots if respectively more than one half and more than one third of the robots exhibit Byzantine failures, starting from the original theorems by Bouzid et al.. Thanks to our formalization, the corresponding COQ developments are quite compact. To our knowledge, these are the first certified (in the sense of formally proved) impossibility results for robot networks

Brief Announcement: Anonymous Obstruction-free (n, k)-Set Agreement with n−k+1 Atomic Read/Write Registers

International audienceThis paper presents an obstruction-free solution to the (n,k)-set agreement problem in an asynchronous anonymous read/write system using solely (n − k + 1) registers. We then extend this algorithm into (i) a space-optimal solution for the repeated version of (n, k)-set agreement, and (ii) an x-obstruction- free solution using (n − k + x) atomic registers (with 1 ≤ x ≤ k < n)

Certified Impossibility Results for Byzantine-Tolerant Mobile Robots

We propose a framework to build formal developments for robot networks using the COQ proof assistant, to state and to prove formally various properties. We focus in this paper on impossibility proofs, as it is natural to take advantage of the COQ higher order calculus to reason about algorithms as abstract objects. We present in particular formal proofs of two impossibility results forconvergence of oblivious mobile robots if respectively more than one half and more than one third of the robots exhibit Byzantine failures, starting from the original theorems by Bouzid et al.. Thanks to our formalization, the corresponding COQ developments are quite compact. To our knowledge, these are the first certified (in the sense of formally proved) impossibility results for robot networks

(anti−Ω x ×Σz)-based k-set Agreement Algorithms

This paper considers the k-set agreement problem in a crash-prone asynchronous message passing system enriched with failure detectors. Two classes of failure detectors have been previously identified as necessary to solve asynchronous k-set agreement: the class anti-leader anti−Ω k and the weak-quorum class Σk. The paper investigates the families of failure detector (anti−Ω x)1≤x≤n and (Σz)1≤z≤n. It characterizesin an n processes system equipped with failure detectors anti−Ω x and Σz for which values of k,x and z k-set-agreement can be solved. While doing so, the paper (1) disproves previous conjunctures about the weakest failure detector to solve k-set-agreement in the asynchronous message passing model and, (2) introduces the first indulgent algorithm that tolerates a majority of processes failures. Keywords: Set-agreement, asynchrony, failure detectors, indulgent algorithms.

Modèles et algorithmes pour les systèmes émergents

Networks of autonomous robots are mobile entities that communicate only through their movements and the observation of their respective positions. They are anonymous, without memory and without a global coordinate system nor a common notion of distance.We focus on the algorithmic study of the problems of gathering and convergence of robots when some of them may be subject to failures.Our first contribution is of geometric nature. We provide a protocol to compute the Weber point of a large class of rotational symmetric configurations.Based on this primitive, we present an algorithm that solves thegathering problem in presence of any number of crash failures.Then, we address the convergence problem when robots may incur byzantine failures which are harder to handle than crash failures. We provide several tight bounds relating the degree of synchronicity of the system to its resiliency.Finally, we study robots that are endowed with memory and we show that this model is stronger than the message passing model.the different node types in an uniformized manner.Our experimental results show that this model is able to take in account the correlations between labels of different node types.Les réseaux de robots autonomes sont des entités mobiles qucommuniquent uniquement travers leurs mouvements et l'observation deleurs positions respectives. Ils sont anonymes, sans mémoire et sanssystème de coordonnées global, ni une notion commune de ladistance.Nous nous concentrons sur l'étude algorithmique des problèmes derassemblement et de convergence des robots quand ils sont sujets despannes.Notre première contribution est de nature géométrique. Nousfournissons un protocole pour calculer le point Weber d'une grandeclasse de configurations qui ont une symétrie rotationnelle.Se basant sur cette primitive, nous présentons un algorithme quirésout le problème du rassemblement en présence de n'importe quelnombre de pannes franches.Ensuite, nous abordons le problème de convergence quand les robotspeuvent subir des pannes byzantines qui sont plus difficiles àmanipuler que les pannes franches. Nous fournissons plusieurs bornesoptimales qui relient le degré de synchronie du système àsa résilience.Enfin, nous Étudions les robots qui sont dotées de mémoire et nousmontrons que ce modèle est plus fort que le modèle de passage demessages.PARIS-BIUSJ-Mathématiques rech (751052111) / SudocSudocFranceF