A new analysis of a self-stabilizing maximum weight matching algorithm with approximation ratio 2

Turau, Volker; Hauck, Bernd

doi:10.1016/j.tcs.2010.11.032

Cited by 8 publications

(3 citation statements)

References 15 publications

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“…Self-stabilizing algorithms for computing maximal matching have been designed in various models (anonymous network [1] or not [14], weighted or unweighted, see [7] for a survey). For an unweighted graph, Hsu and Huang [9] gave the first self-stabilizing algorithm and proved a bound of O(n 3 ) on the number of moves under a sequential adversarial daemon.…”

Section: State Of the Artmentioning

confidence: 99%

A Self-Stabilizing Algorithm for Maximal Matching in Link-Register Model

Cohen

Manoussakis

Pilard

et al. 2018

Structural Information and Communication Complexity

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In the matching problem, each node maintains a pointer to one of its neighbor or to null, and a maximal matching is computed when each node points either to a neighbor that itself points to it (they are then called married), or to null, in which case no neighbor can also point to null. This paper presents a self-stabilizing distributed algorithm to compute a maximal matching in the link-register model under read/write atomicity, with complexity O(n∆ 3 ) moves under the adversarial distributed daemon, where ∆ is the maximum degree of the graph.

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Section: State Of the Artmentioning

confidence: 99%

A Self-Stabilizing Algorithm for Maximal Matching in Link-Register Model

Cohen

Manoussakis

Pilard

et al. 2018

Structural Information and Communication Complexity

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“…sequential or distributed). Turau and Hauck [22] gave a modified version of the previous algorithm that stabilizes after O(nm) moves under any adversarial daemon.…”

Section: Related Workmentioning

confidence: 99%

A Self-Stabilizing Algorithm for Maximal Matching in Anonymous Networks

Cohen

Lefèvre

Maamra

et al. 2016

Parallel Process. Lett.

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We propose a self-stabilizing algorithm for computing a maximal matching in an anonymous network. The complexity is O(n 3 ) moves with high probability, under the adversarial distributed daemon. In this algorithm, each node can determine whether one of its neighbors points to it or to another node, leading to a contradiction with the anonymous assumption. To solve this problem, we provide under the classical link-register model, a self-stabilizing algorithm that gives a unique name to a link such that this name is shared by both extremities of the link.

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“…Manne et al [MM07] proposed the first self-stabilizing algorithm for the maximum weighted matching problem achieving an approximation ratio of 2 in a (exponential) bounded number of steps under a centralized daemon and a distributed daemon. Turau et al [TH11b] gave a new analysis of the algorithm of Manne et al [MM07]. They showed that this algorithm converges in O(nm) steps under a centralized daemon and an unfair distributed daemon.…”

Section: Related Workmentioning

confidence: 99%

Self-stabilizing Algorithms for Connected Vertex Cover and Clique Decomposition Problems

Laforest

Rovedakis

2014

Lecture Notes in Computer Science

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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 Connected Vertex Cover problem, a generalization of the classical minimum Vertex Cover problem, which allows to obtain a connected backbone. Recently, Delbot et al. [DLP13] proposed a new centralized algorithm with a constant approximation ratio of 2 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. to route messages in the network. Routing messages are only exchanged inside the backbone, instead of being broadcasted to the entire network. To this end, the backbone must be connected. The construction and the maintenance of a virtual backbone is often realized by constructing a Connected Dominating Set. A Connected Dominating Set (CDS) of a graph G = (V, E) is a set of nodes S ⊆ V such that G[S] (the graph induced by S in G) is connected and each node in V − S has at least one neighbor in S. Nodes from S are responsible of routing the messages in the network, whereas nodes in V − S communicate by exchanging messages through neighbors in S. In order to minimize the use of resources, the size of the backbone (and thus of the CDS) is minimized. This problem is NP-hard [GJ79] and has been extensively studied due to its importance for communications in wireless networks. Many algorithms have been proposed in centralized systems (e.g., see [BDTC05] for a survey). In addition to message routing, there is the problem of network security. Indeed, a faulty node infected by a virus or an unscrupulous user can be at the origin of flooding or a malicious attack. Thus, it is necessary to monitor all network communications to identify these situations, as soon as possible, in order to isolate this node. A CDS S will not support this feature since two nodes in V − S can be neighbors, i.e, V − S is not always an independent set.In order to monitor all network communications, we can consider the Vertex Cover problem. A vertex cover of a graph G = (V, E) is a set of nodes S ⊆ V such that each edge e = uv is covered by S, i.e., u ∈ S or v ∈ S (or both). A vertex cover is optimal if it's size is minimum. This is a classical NP-complete problem [GJ79] that can be approximated with a ratio of...

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A new analysis of a self-stabilizing maximum weight matching algorithm with approximation ratio 2

Cited by 8 publications

References 15 publications

A Self-Stabilizing Algorithm for Maximal Matching in Link-Register Model

A Self-Stabilizing Algorithm for Maximal Matching in Link-Register Model

A Self-Stabilizing Algorithm for Maximal Matching in Anonymous Networks

Self-stabilizing Algorithms for Connected Vertex Cover and Clique Decomposition Problems

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