A greedy algorithm for the minimum $$2$$ 2 -connected $$m$$ m -fold dominating set problem

Shi, Yishuo; Zhang, Yaping; Zhang, Zhao; Wu, Weili

doi:10.1007/s10878-014-9720-6

Cited by 36 publications

(32 citation statements)

References 24 publications

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“…general (2, m) 4 + ln(δ + m − 2) + 2 ln(2 + ln(δ + m − 2)) [24] UDG (2, 1) 72 [29] UDG ( As a consequence, we have the following result. …”

Section: Preliminariesmentioning

confidence: 73%

“…In a recent paper, we [24] proposed a ln(δ + m − 2) + o(ln δ) -approximation algorithm for the minimum (2, m)-CDS problem on a general graph, where δ is the maximum degree of the graph. Based on it, the algorithm in this paper has performance ratio ln(δ + m − 2) + o(ln δ).…”

Section: Definition 11 ((K M)-cds)mentioning

confidence: 99%

“…Previous to this work, Wang et al [30] obtained a constant approximation algorithm for (3, m)-CDS on UDG, and the ratio is further improved in their recent work [31], which is 5α. For example, if the value of α in paper [24] is used, their algorithm for (3, 3)-CDS on UDG has performance ratio 62.3. Our ratio improves theirs by a large amount.…”

Section: Definition 11 ((K M)-cds)mentioning

confidence: 99%

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Fault-Tolerant Virtual Backbone in Heterogeneous Wireless Sensor Network

Zhou

Zhang

Tang

et al. 2017

IEEE/ACM Trans. Networking

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To save energy and alleviate interferences in a wireless sensor network, the usage of virtual backbone was proposed. Because of accidental damages or energy depletion, it is desirable to construct a fault tolerant virtual backbone, which can be modeled as a k-connected m-fold dominating set (abbreviated as (is adjacent with at least m nodes in C and the subgraph of G induced by C is k-connected. In this paper, we present an approximation algorithm for the minimum (3, m)-CDS problem with m ≥ 3. The performance ratio is at most γ, where γ = α + 8 + 2 ln(2α − 6) for α ≥ 4 and γ = 3α + 2 ln 2 for α < 4, and α is the performance ratio for the minimum (2, m)-CDS problem. Using currently best known value of α, the performance ratio is ln δ + o(ln δ), where δ is the maximum degree of the graph, which is asymptotically best possible in view of the non-approximability of the problem. This is the first performance-guaranteed algorithm for the minimum (3, m)-CDS problem on a general graph. Furthermore, applying our algorithm on a unit disk graph which models a homogeneous wireless sensor network, the performance ratio is less than 27, improving previous ratio 62.3 by a large amount for the (3, m)-CDS problem on a unit disk graph.

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“…general (2, m) 4 + ln(δ + m − 2) + 2 ln(2 + ln(δ + m − 2)) [24] UDG (2, 1) 72 [29] UDG ( As a consequence, we have the following result. …”

Section: Preliminariesmentioning

confidence: 73%

Section: Definition 11 ((K M)-cds)mentioning

confidence: 99%

Section: Definition 11 ((K M)-cds)mentioning

confidence: 99%

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Fault-Tolerant Virtual Backbone in Heterogeneous Wireless Sensor Network

Zhou

Zhang

Tang

et al. 2017

IEEE/ACM Trans. Networking

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“…Theorem 2 [25]: The algorithm for the minimum (2, m)-CDS has a performance ratio α + 2(1 + ln α) for m > 3, where α is the approximation ratio for the minimum (1, m)-CDS and 12.46 for m = 3.…”

Section: Performance Analysismentioning

confidence: 99%

“…Theorem 6: Algorithm 1 is a 5r-approximation for computing (3, m)-CDS, for m > 3, where r is the approximation ratio for computing the minimum (2, m)-CDS in [25].…”

Section: Performance Analysismentioning

confidence: 99%

A New Constant Factor Approximation to Construct Highly Fault-Tolerant Connected Dominating Set in Unit Disk Graph

Wang

Liu

Kim

et al. 2017

IEEE/ACM Trans. Networking

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This paper proposes a new polynomial time constant factor approximation algorithm for a more-a-decade-long open NP-hard problem, the minimum four-connected m-dominating set problem in unit disk graph (UDG) with any positive integer m ≥ 1 for the first time in the literature. We observe that it is difficult to modify the existing constant factor approximation algorithm for the minimum three-connected m-dominating set problem to solve the minimum four-connected m-dominating set problem in UDG due to the structural limitation of Tutte decomposition, which is the main graph theory tool used by Wang et al. to design their algorithm. To resolve this issue, we first reinvent a new constant factor approximation algorithm for the minimum three-connected m-dominating set problem in UDG and later use this algorithm to design a new constant factor approximation algorithm for the minimum four-connected m-dominating set problem in UDG.

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Fault Tolerant Multiple Dominating Set Constructions for Wireless Ad-hoc Networks

Papry

Rahman

2022

Advanced Information Networking and Applications

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A greedy algorithm for the minimum $$2$$ 2 -connected $$m$$ m -fold dominating set problem

Cited by 36 publications

References 24 publications

Fault-Tolerant Virtual Backbone in Heterogeneous Wireless Sensor Network

Fault-Tolerant Virtual Backbone in Heterogeneous Wireless Sensor Network

A New Constant Factor Approximation to Construct Highly Fault-Tolerant Connected Dominating Set in Unit Disk Graph

Fault Tolerant Multiple Dominating Set Constructions for Wireless Ad-hoc Networks

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