2003
DOI: 10.1002/net.10097
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A polynomial‐time approximation scheme for the minimum‐connected dominating set in ad hoc wireless networks

Abstract: A connected dominating set in a graph is a subset of vertices such that every vertex is either in the subset or adjacent to a vertex in the subset and the subgraph induced by the subset is connected. A minimum-connected dominating set is such a vertex subset with minimum cardinality. An application in ad hoc wireless networks requires the study of the minimum-connected dominating set in unit-disk graphs. In this paper, we design a (1 ؉ 1/s)-approximation for the minimum-connected dominating set in unit-disk gr… Show more

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Cited by 289 publications
(125 citation statements)
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“…In such graphs, nodes are unit circles, where any two nodes are said to be adjacent, if and only if, they reside within the unit distance. As data transmission is a major energy consumer in WSNs, most current algorithms address the Minimum sized CDS (MCDS) to reduce global communication distances and transmission rates [12].…”
Section: Related Workmentioning
confidence: 99%
“…In such graphs, nodes are unit circles, where any two nodes are said to be adjacent, if and only if, they reside within the unit distance. As data transmission is a major energy consumer in WSNs, most current algorithms address the Minimum sized CDS (MCDS) to reduce global communication distances and transmission rates [12].…”
Section: Related Workmentioning
confidence: 99%
“…Computing a minimum connected dominating set (MCDS) is an NP-Hard problem in general graphs [11] and in unitdisk graphs [11]. A PTAS for MCDS in unit-disk graphs has been found in [6].…”
Section: Dominating Set and Independent Setmentioning
confidence: 99%
“…MCDS has an O(log ∆) approximation ratio in regular graphs, where ∆ is the maximum number of neighbors of a node. Recently, Cheng et al [10] proposed a polynomial time approximation scheme (PTAS) for the minimum CDS in unit disk graphs. Given a network of size n and a small parameter s, Cheng et al designed a (1 + 1/s)-approximation with running time n O((s log s) 2 ) .…”
Section: Dominating Set and Its Extensionsmentioning
confidence: 99%