384 research outputs found
Self-stabilizing algorithms for Connected Vertex Cover and Clique decomposition problems
In many wireless networks, there is no fixed physical backbone nor
centralized network management. The nodes of such a network have to
self-organize in order to maintain a virtual backbone used to route messages.
Moreover, any node of the network can be a priori at the origin of a malicious
attack. Thus, in one hand the backbone must be fault-tolerant and in other hand
it can be useful to monitor all network communications to identify an attack as
soon as possible. We are interested in the minimum \emph{Connected Vertex
Cover} problem, a generalization of the classical minimum Vertex Cover problem,
which allows to obtain a connected backbone. Recently, Delbot et
al.~\cite{DelbotLP13} proposed a new centralized algorithm with a constant
approximation ratio of for this problem. In this paper, we propose a
distributed and self-stabilizing version of their algorithm with the same
approximation guarantee. To the best knowledge of the authors, it is the first
distributed and fault-tolerant algorithm for this problem. The approach
followed to solve the considered problem is based on the construction of a
connected minimal clique partition. Therefore, we also design the first
distributed self-stabilizing algorithm for this problem, which is of
independent interest
Survey of Distributed Decision
We survey the recent distributed computing literature on checking whether a
given distributed system configuration satisfies a given boolean predicate,
i.e., whether the configuration is legal or illegal w.r.t. that predicate. We
consider classical distributed computing environments, including mostly
synchronous fault-free network computing (LOCAL and CONGEST models), but also
asynchronous crash-prone shared-memory computing (WAIT-FREE model), and mobile
computing (FSYNC model)
Design of Self-Stabilizing Approximation Algorithms via a Primal-Dual Approach
Self-stabilization is an important concept in the realm of fault-tolerant distributed computing. In this paper, we propose a new approach that relies on the properties of linear programming duality to obtain self-stabilizing approximation algorithms for distributed graph optimization problems. The power of this new approach is demonstrated by the following results:
- A self-stabilizing 2(1+?)-approximation algorithm for minimum weight vertex cover that converges in O(log? /(?log log ?)) synchronous rounds.
- A self-stabilizing ?-approximation algorithm for maximum weight independent set that converges in O(?+log^* n) synchronous rounds.
- A self-stabilizing ((2?+1)(1+?))-approximation algorithm for minimum weight dominating set in ?-arboricity graphs that converges in O((log?)/?) synchronous rounds. In all of the above, ? denotes the maximum degree. Our technique improves upon previous results in terms of time complexity while incurring only an additive O(log n) overhead to the message size. In addition, to the best of our knowledge, we provide the first self-stabilizing algorithms for the weighted versions of minimum vertex cover and maximum independent set
Local algorithms : Self-stabilization on speed
Non peer reviewe
Plane Formation by Synchronous Mobile Robots in the Three Dimensional Euclidean Space
Creating a swarm of mobile computing entities frequently called robots,
agents or sensor nodes, with self-organization ability is a contemporary
challenge in distributed computing. Motivated by this, we investigate the plane
formation problem that requires a swarm of robots moving in the three
dimensional Euclidean space to land on a common plane. The robots are fully
synchronous and endowed with visual perception. But they do not have
identifiers, nor access to the global coordinate system, nor any means of
explicit communication with each other. Though there are plenty of results on
the agreement problem for robots in the two dimensional plane, for example, the
point formation problem, the pattern formation problem, and so on, this is the
first result for robots in the three dimensional space. This paper presents a
necessary and sufficient condition for fully-synchronous robots to solve the
plane formation problem that does not depend on obliviousness i.e., the
availability of local memory at robots. An implication of the result is
somewhat counter-intuitive: The robots cannot form a plane from most of the
semi-regular polyhedra, while they can form a plane from every regular
polyhedron (except a regular icosahedron), whose symmetry is usually considered
to be higher than any semi-regular polyhedrdon
A local 2-approximation algorithm for the vertex cover problem
We present a distributed 2-approximation algorithm for the minimum vertex cover problem. The algorithm is deterministic, and it runs in (Î + 1)2 synchronous communication rounds, where Î is the maximum degree of the graph. For Î = 3, we give a 2-approximation algorithm also for the weighted version of the problem.Peer reviewe
Local approximability of max-min and min-max linear programs
In a max-min LP, the objective is to maximise Ï subject to Ax †1, Cx â„ Ï1, and x â„ 0. In a min-max LP, the objective is to minimise Ï subject to Ax †Ï1, Cx â„ 1, and x â„ 0. The matrices A and C are nonnegative and sparse: each row ai of A has at most ÎI positive elements, and each row ck of C has at most ÎK positive elements. We study the approximability of max-min LPs and min-max LPs in a distributed setting; in particular, we focus on local algorithms (constant-time distributed algorithms). We show that for any ÎI â„ 2, ÎK â„ 2, and Δ > 0 there exists a local algorithm that achieves the approximation ratio ÎI (1 â 1/ÎK) + Δ. We also show that this result is the best possible: no local algorithm can achieve the approximation ratio ÎI (1 â 1/ÎK) for any ÎI â„ 2 and ÎK â„ 2.Peer reviewe
Pulse propagation, graph cover, and packet forwarding
We study distributed systems, with a particular focus on graph problems and fault tolerance. Fault-tolerance in a microprocessor or even System-on-Chip can be improved by using a fault-tolerant pulse propagation design. The existing design TRIX achieves this goal by being a distributed system consisting of very simple nodes. We show that even in the typical mode of operation without faults, TRIX performs significantly better than a regular wire or clock tree: Statistical evaluation of our simulated experiments show that we achieve a skew with standard deviation of O(log log H), where H is the height of the TRIX grid. The distance-r generalization of classic graph problems can give us insights on how distance affects hardness of a problem. For the distance-r dominating set problem, we present both an algorithmic upper and unconditional lower bound for any graph class with certain high-girth and sparseness criteria. In particular, our algorithm achieves a O(r·f(r))-approximation in time O(r), where f is the expansion function, which correlates with density. For constant r, this implies a constant approximation factor, in constant time. We also show that no algorithm can achieve a (2r + 1 â ÎŽ)-approximation for any ÎŽ > 0 in time O(r), not even on the class of cycles of girth at least 5r. Furthermore, we extend the algorithm to related graph cover problems and even to a different execution model. Furthermore, we investigate the problem of packet forwarding, which addresses the question of how and when best to forward packets in a distributed system. These packets are injected by an adversary. We build on the existing algorithm OED to handle more than a single destination. In particular, we show that buffers of size O(log n) are sufficient for this algorithm, in contrast to O(n) for the naive approach.Wir untersuchen verteilte Systeme, mit besonderem Augenmerk auf Graphenprobleme und Fehlertoleranz. Fehlertoleranz auf einem System-on-Chip (SoC) kann durch eine fehlertolerante Puls- Weiterleitung verbessert werden. Das bestehende Puls-Weiterleitungs-System TRIX toleriert Fehler indem es ein verteiltes System ist das nur aus sehr einfachen Knoten besteht. Wir zeigen dass selbst im typischen, fehlerfreien Fall TRIX sich weitaus besser verhĂ€lt als man naiverweise erwarten wĂŒrde: Statistische Analysen unserer simulierten Experimente zeigen, dass der Verzögerungs-Unterschied eine Standardabweichung von lediglich O(log logH) erreicht, wobei H die Höhe des TRIX-Netzes ist. Das Generalisieren einiger klassischer Graphen-Probleme auf Distanz r kann uns neue Erkenntnisse bescheren ĂŒber den Zusammenhang zwischen Distanz und KomplexitĂ€t eines Problems. FĂŒr das Problem der dominierenden Mengen auf Distanz r zeigen wir sowohl eine algorithmische obere Schranke als auch eine bedingungsfreie untere Schranke fĂŒr jede Klasse von Graphen, die bestimmte Eigenschaften an Umfang und Dichte erfĂŒllt. Konkret erreicht unser Algorithmus in Zeit O(r) eine AnnĂ€herungsgĂŒte von O(r · f(r)). FĂŒr konstante r bedeutet das, dass der Algorithmus in konstanter Zeit eine AnnĂ€herung konstanter GĂŒte erreicht. Weiterhin zeigen wir, dass kein Algorithmus in Zeit O(r) eine AnnĂ€herungsgĂŒte besser als 2r + 1 erreichen kann, nicht einmal in der Klasse der Kreis-Graphen von Umfang mindestens 5r. Weiterhin haben wir das Paketweiterleitungs-Problem untersucht, welches sich mit der Frage beschĂ€ftigt, wann genau Pakete in einem verteilten System idealerweise weitergeleitetwerden sollten. Die Paketewerden dabei von einem Gegenspieler eingefĂŒgt. Wir bauen auf dem existierenden Algorithmus OED auf, um mehr als ein Paket-Ziel beliefern zu können. Dadurch zeigen wir, dass Paket-Speicher der GröĂe O(log n) fĂŒr dieses Problem ausreichen, im Gegensatz zu den Paket-Speichern der GröĂe O(n) die fĂŒr einen naiven Ansatz nötig wĂ€ren
Ant-Inspired Density Estimation via Random Walks
Many ant species employ distributed population density estimation in
applications ranging from quorum sensing [Pra05], to task allocation [Gor99],
to appraisal of enemy colony strength [Ada90]. It has been shown that ants
estimate density by tracking encounter rates -- the higher the population
density, the more often the ants bump into each other [Pra05,GPT93].
We study distributed density estimation from a theoretical perspective. We
prove that a group of anonymous agents randomly walking on a grid are able to
estimate their density within a small multiplicative error in few steps by
measuring their rates of encounter with other agents. Despite dependencies
inherent in the fact that nearby agents may collide repeatedly (and, worse,
cannot recognize when this happens), our bound nearly matches what would be
required to estimate density by independently sampling grid locations.
From a biological perspective, our work helps shed light on how ants and
other social insects can obtain relatively accurate density estimates via
encounter rates. From a technical perspective, our analysis provides new tools
for understanding complex dependencies in the collision probabilities of
multiple random walks. We bound the strength of these dependencies using
of the underlying graph. Our results extend beyond
the grid to more general graphs and we discuss applications to size estimation
for social networks and density estimation for robot swarms
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