Linear self-stabilizing algorithms for the independent and dominating set problems using an unfair distributed scheduler

Turau, Volker

doi:10.1016/j.ipl.2007.02.013

Cited by 68 publications

(33 citation statements)

References 8 publications

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“…Three self-stabilizing algorithms for the maximal independent set problem were proposed in the literature (see also [14]). The first one was proposed by Shukla et al in [24], the second one by Ikeda et al in [18], and the third one by Turau in [25]. Henceforth we will refer to these algorithms as Shukla, Ikeda and Turau.…”

Section: Competitor Algorithmsmentioning

confidence: 99%

FrogCOL and FrogMIS: new decentralized algorithms for finding large independent sets in graphs

2015

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Finding large (and generally maximal) independent sets of vertices in a given graph is a fundamental problem in distributed computing. Applications include, for example, facility location and backbone formation in wireless ad hoc networks. In this paper we study a decentralized (or distributed) algorithm inspired by the calling behaviour of male Japanese tree frogs, originally introduced for the graph coloring problem, for its potential usefulness in the context of finding large independent sets. Moreover, we adapt this algorithm to directly produce maximal independent sets without the necessity of first producing a graph coloring solution. Both algorithms are compared to a wide range of decentralized algorithms from the literature on a diverse set of benchmark instances for the maximal independent set problem. The results show that both algorithms compare very favorably to their competitors.

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Section: Competitor Algorithmsmentioning

confidence: 99%

FrogCOL and FrogMIS: new decentralized algorithms for finding large independent sets in graphs

2015

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“…A weakly connected dominating set [11][12][13][14] is similar to connected dominating set, and allows nodes to form connected clusters. It is a dominating set where the subgraph of the close neighborhood of the set is connected.…”

Section: Our Goal In This Papermentioning

confidence: 99%

Distributed fault tolerant computation of weakly connected dominating set in ad hoc networks

Wang

Srimani

2009

J Supercomput

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Our purpose in this paper is to propose a self-stabilizing protocol for weakly connected dominating set (WCDS) set in a given ad hoc network graph. WCDS is a particular variant of graph domination predicates which play an important role in routing in ad hoc networks. There are many variants of domination problems in bidirectional networks; WCDS is also useful in forming clusters in ad hoc networks. There are many heuristic and distributed algorithms to compute WCDS in network graphs while almost all of them will need complete information about the network topology and most of them are not fault tolerant or mobility tolerant. Self-stabilization is a protocol design paradigm that is especially useful in resource constrained infrastructure-less networks since nodes can make moves based on local knowledge only and yet a global task is accomplished in a fault tolerant manner; it also facilitates for nodes to enter and exit the network freely. There exist selfstabilizing protocols for minimal spanning tree, total domination, and others. We have shown that the paradigm is capable of designing a protocol for WCDS. Our objective is to mathematically prove the correctness and the convergence of the protocol in any worst-case scenario, as is usually done for self-stabilizing protocols for other graph predicates used for ad hoc networks.

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“…To the best of our knowledge, this has been the only publication on (f, g)-alliances up to now. However, there have been results on particular instances of (minimal) (f, g)-alliances, e.g., [9,[13][14][15]. All of these consider arbitrary identified networks; however a safely converging solution is given only in [9].…”

Section: Introductionmentioning

confidence: 99%

“…Srimani and Xu [13] give a self-stabilizing algorithm to compute a minimal global defensive alliance in O(n 3 ) steps; however, they assume a central daemon. Turau [14] gives a self-stabilizing algorithm to compute a minimal dominating set in 9n steps, assuming an unfair (distributed) daemon. Wang et al [15] give a self-stabilizing algorithm to compute a minimal k-domination set in O(n 2 ) steps, assuming a central daemon.…”

Section: Introductionmentioning

confidence: 99%

Self-stabilizing (f,g)-Alliances with Safe Convergence

Carrier

Datta

Devismes

et al. 2013

Lecture Notes in Computer Science

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Abstract. Given two functions f and g mapping nodes to non-negative integers, we give a silent self-stabilizing algorithm that computes a minimal (f, g)-alliance in an asynchronous network with unique node IDs, assuming that every node p has a degree at least g(p) and satisfies f (p) ≥ g(p). Our algorithm is safely converging in the sense that starting from any configuration, it first converges to a (not necessarily minimal) (f, g)-alliance in at most four rounds, and then continues to converge to a minimal one in at most 5n+4 additional rounds, where n is the size of the network. Our algorithm is written in the shared memory model. It is proven assuming an unfair (distributed) daemon. Its memory requirement is O(log n) bits per process, and it takes O(∆ 3 n) steps to stabilize, where ∆ is the degree of the network.

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Linear self-stabilizing algorithms for the independent and dominating set problems using an unfair distributed scheduler

Cited by 68 publications

References 8 publications

FrogCOL and FrogMIS: new decentralized algorithms for finding large independent sets in graphs

FrogCOL and FrogMIS: new decentralized algorithms for finding large independent sets in graphs

Distributed fault tolerant computation of weakly connected dominating set in ad hoc networks

Self-stabilizing (f,g)-Alliances with Safe Convergence

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