Approximation Algorithm for Minimum Weight Fault-Tolerant Virtual Backbone in Unit Disk Graphs

Shi, Yishuo; Zhang, Zhao; Mo, Yuchang; Du, Ding‐Zhu

doi:10.1109/tnet.2016.2607723

Cited by 36 publications

(25 citation statements)

References 42 publications

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“…In the present paper, we give the first nontrivial approximation algorithm for this problem (in Section 5.1), and hence the algorithm of Shi, Zhang, and Du [23] achieves the claimed approximation guarantee only when combined with our result. In their journal version [24], this fact is described. In the second step of converting the m-dominating set into a k-connected m-dominating set, the approach of [23,24] and ours are different.…”

Section: Our Resultsmentioning

confidence: 98%

Approximation Algorithms for Highly Connected Multi-dominating Sets in Unit Disk Graphs

Fukunaga

2017

Algorithmica

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Given an undirected graph on a node set V and positive integers k and m, a k-connected m-dominating set ((k, m)-CDS) is defined as a subset S of V such that each node in V \ S has at least m neighbors in S, and a k-connected subgraph is induced by S. The weighted (k, m)-CDS problem is to find a minimum weight (k, m)-CDS in a given node-weighted graph. The problem is called the unweighted (k, m)-CDS problem if the objective is to minimize the cardinality of a (k, m)-CDS. These problems have been actively studied for unit disk graphs, motivated by the application of constructing a virtual backbone in a wireless ad hoc network. In this paper, we consider the case in which k ≤ m, and we present a simple O(k5 k )-approximation algorithm for the unweighted (k, m)-CDS problem, and a primal-dual O(k 2 log k)-approximation algorithm for the weighted (k, m)-CDS problem.A CDS does not give a fault-tolerant virtual backbone network. This is because a CDS is only required to be connected, and each node outside a CDS is required to have only one neighbor in the CDS. Hence, if a backbone node fails, the virtual backbone network may be disconnected, or a nonbackbone node may lose access to the virtual backbone network. To overcome this disadvantage, Dai and Wu [10] proposed replacing a CDS by a k-connected k-dominating set, and they addressed the problem of finding a minimum k-connected k-dominating set in a unit disk graph. For a graph with the node set V , a subset S of V is called k-connected if the subgraph induced by S is kconnected (i.e., it is connected even if any k − 1 nodes are removed), and is called k-dominating if each node v ∈ V \ S has k neighbors in S. Triggered by their study, much attention has been paid to this problem, extending the notion of a k-connected k-dominating set to a more-general k-connected m-dominating set ((k, m)-CDS).The problem of finding a minimum cardinality (k, m)-CDS in a unit disk graph is called the unweighted (k, m)-CDS problem. If each node is given a nonnegative weight, and the objective is to minimize the weight of a (k, m)-CDS, then this is called the weighted (k, m)-CDS problem. As for the unweighted (k, m)-CDS problem, several constant-approximation algorithms were given for k ≤ 3 [21,22,26,27,30]. As for the weighted (k, m)-CDS problem, there are several constantapproximation algorithms for k = m = 1 [2, 31], but no approximation algorithm was known for the case of (k, m) = (1, 1) before our study (see Section 2 for more literature reviews).After these previous studies, a natural question arises as to whether there is a constantapproximation algorithm for the unweighted (k, m)-CDS problem with k ≥ 4, and for the weighted problem with (k, m) = (1, 1). For the unweighted problem, this question has been already addressed in both [26] and [27].

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Section: Our Resultsmentioning

confidence: 98%

Approximation Algorithms for Highly Connected Multi-dominating Sets in Unit Disk Graphs

Fukunaga

2017

Algorithmica

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“…We consider the Unit Disk Graph (UDG) model [ 12 , 29 , 30 ], where the network is defined by

. The vertices in V are embedded in the Euclidean plane.…”

Section: Simulation Resultsmentioning

confidence: 99%

New Computation of Resolving Connected Dominating Sets in Weighted Networks

Dapena

Iglesia

Vázquez-Araújo

et al. 2019

Entropy

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In this paper we focus on the issue related to finding the resolving connected dominating sets (RCDSs) of a graph, denoted by G. The connected dominating set (CDS) is a connected subset of vertices of G selected to guarantee that all vertices in the graph are connected to vertices in the CDS. The connected dominating set with minimum cardinality, or minimum CDS (MCDS), is an adequate virtual backbone for information interchange in a network. When distinct vertices of G have also distinct representations with respect to a subset of vertices in the MCDS, it is said that the MCDS includes a resolving set (RS) of G. With this work, we explore different strategies to find the RCDS with minimum cardinality in complex networks where the vertices have different importances.

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“…In theory, a VB is a subset of sensor nodes in a WSN that meets the following requirements [15]. First, each node in a WSN is adjacent to a node in this subset.…”

Section: Introductionmentioning

confidence: 99%

Construction of Quality Virtual Backbones with Link Fault Tolerance in Wireless Sensor Networks

Liang

Zhang

2021

Wireless Communications and Mobile Computing

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Wireless sensor networks (WSNs) are extensively utilized in various circumstances. For applications, the construction of the virtual backbones (VBs) of WSNs has attracted considerable attention in this field. Generally, a homogeneous WSN is formulated as a unit disk graph (UDG), and the VB of the corresponding WSN is modeled as a connected dominating set (CDS) in the UDG. In certain applications, communication between sensors in a network may fail for various reasons, such as sensor movement, signal interference, and the appearance of obstacles. Consequently, a CDS in a UDG should possess fault tolerance on the edges. In this paper, we introduce a new concept called the 2 edge-connected 2 edge-dominating set ( 2 , 2 -ECDS); then, we design an approximation algorithm for computing 2 , 2 -ECDSs in UDGs, the performance ratio of which is 30.51. By means of simulations, we compare our algorithm and existing algorithms in terms of the CDS size, running time, success rate, and network lifetime. The simulation results indicate that our algorithm exhibits better performance and is more suitable for constructing a VB with edge fault tolerance in a WSN.

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Approximation Algorithm for Minimum Weight Fault-Tolerant Virtual Backbone in Unit Disk Graphs

Cited by 36 publications

References 42 publications

Approximation Algorithms for Highly Connected Multi-dominating Sets in Unit Disk Graphs

Approximation Algorithms for Highly Connected Multi-dominating Sets in Unit Disk Graphs

New Computation of Resolving Connected Dominating Sets in Weighted Networks

Construction of Quality Virtual Backbones with Link Fault Tolerance in Wireless Sensor Networks

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