A Self-stabilizing Approximation Algorithm for Vertex Cover in Anonymous Networks

Turau, Volker; Hauck, Bernd

doi:10.1007/978-3-642-05118-0_24

Cited by 6 publications

(6 citation statements)

References 7 publications

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“…In [ 39 ], Turau et al have introduced two self-stabilizing vertex cover algorithms, which run on anonymous networks. Both algorithms are based on the study given in [ 25 ] which cannot exceed the 3-approximation ratio by using the matching method on the anonymous networks proved by [ 40 ].…”

Section: Related Workmentioning

confidence: 99%

“…In addition to the algorithms we proposed, we implemented the algorithms of Kiniwa [ 38 ] and Turau [ 39 ], which are state-of-the-art algorithms for self-stabilizing vertex cover domain. To provide the capacity constraint for the algorithms of Kiniwa and Turau, we added

and

variables and two rules which are shown in Algorithm 3.…”

Section: Performance Evaluationmentioning

confidence: 99%

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Self-Stabilizing Capacitated Vertex Cover Algorithms for Internet-of-Things-Enabled Wireless Sensor Networks

Yigit

Dağdeviren

Challenger

2022

Sensors

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Wireless sensor networks (WSNs) achieving environmental sensing are fundamental communication layer technologies in the Internet of Things. Battery-powered sensor nodes may face many problems, such as battery drain and software problems. Therefore, the utilization of self-stabilization, which is one of the fault-tolerance techniques, brings the network back to its legitimate state when the topology is changed due to node leaves. In this technique, a scheduler decides on which nodes could execute their rules regarding spatial and temporal properties. A useful graph theoretical structure is the vertex cover that can be utilized in various WSN applications such as routing, clustering, replica placement and link monitoring. A capacitated vertex cover is the generalized version of the problem which restricts the number of edges covered by a vertex by applying a capacity constraint to limit the covered edge count. In this paper, we propose two self-stabilizing capacitated vertex cover algorithms for WSNs. To the best of our knowledge, these algorithms are the first attempts in this manner. The first algorithm is stabilized under an unfair distributed scheduler (that is, the scheduler which does not grant all enabled nodes to make their moves but guarantees the global progress of the system) at most O(n2) step, where n is the count of nodes. The second algorithm assumes 2-hop (degree 2) knowledge about the network and runs under the unfair scheduler, which subsumes the synchronous and distributed fair scheduler and stabilizes itself after O(n) moves in O(n) step, which is acceptable for most WSN setups. We theoretically analyze the algorithms to provide proof of correctness and their step complexities. Moreover, we provide simulation setups by applying IRIS sensor node parameters and compare our algorithms with their counterparts. The gathered measurements from the simulations revealed that the proposed algorithms are faster than their competitors, use less energy and offer better vertex cover solutions.

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Section: Related Workmentioning

confidence: 99%

and

variables and two rules which are shown in Algorithm 3.…”

Section: Performance Evaluationmentioning

confidence: 99%

Self-Stabilizing Capacitated Vertex Cover Algorithms for Internet-of-Things-Enabled Wireless Sensor Networks

Yigit

Dağdeviren

Challenger

2022

Sensors

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“…To overcome this difficulty, authors assume that every two adjacent nodes share a private register containing an incorruptible link's number. Note that this problem does not appear for the vertex cover problem [21] or the independent set problem [20] even in anonymous networks (see [12] for a survey). Indeed, in these kind of problems, we do not try to build a set of edges, but a set of nodes.…”

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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“…This algorithm is based on the construction of a maximal matching which allows to obtain a 2-approximation vertex cover by selecting the extremities of the matching edges. Turau et al [TH11a] considered the same problem in anonymous networks and gave an 3-approximation algorithm under a distributed daemon. Since it is impossible to construct a maximal matching in an anonymous network, this algorithm establishes first a bicolored graph of the network allowing then to construct a maximal matching to obtain a vertex cover.…”

Section: Related Workmentioning

confidence: 99%

“…Turau [Tur10] designed a self-stabilizing vertex cover algorithm with approximation ratio of 2 in anonymous networks under an unfair distributed daemon. This algorithm uses the algorithm in [TH11a] executed several times on parts of the graph to improve the quality of the constructed solution.…”

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 Self-stabilizing Approximation Algorithm for Vertex Cover in Anonymous Networks

Cited by 6 publications

References 7 publications

Self-Stabilizing Capacitated Vertex Cover Algorithms for Internet-of-Things-Enabled Wireless Sensor Networks

Self-Stabilizing Capacitated Vertex Cover Algorithms for Internet-of-Things-Enabled Wireless Sensor Networks

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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