A PTAS for minimum weighted connected vertex cover $$P_3$$ P 3 problem in 3-dimensional wireless sensor networks

Limin Wang (), Wenxue Du (), Zhao Zhang () and Xiaoyan Zhang ()
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Limin Wang: Nanjing Normal University
Wenxue Du: Anhui University
Zhao Zhang: Zhejiang Normal University
Xiaoyan Zhang: Nanjing Normal University

Journal of Combinatorial Optimization, 2017, vol. 33, issue 1, No 7, 106-122

Abstract: Abstract Given a connected and weighted graph $$G=(V, E)$$ G = ( V , E ) with each vertex v having a nonnegative weight w(v), the minimum weighted connected vertex cover $$P_{3}$$ P 3 problem $$(MWCVCP_{3})$$ ( M W C V C P 3 ) is required to find a subset C of vertices of the graph with minimum total weight, such that each path with length 2 has at least one vertex in C, and moreover, the induced subgraph G[C] is connected. This kind of problem has many applications concerning wireless sensor networks and ad hoc networks. When homogeneous sensors are deployed into a three-dimensional space instead of a plane, the mathematical model for the sensor network is a unit ball graph instead of a unit disk graph. In this paper, we propose a new concept called weak c-local and give the first polynomial time approximation scheme (PTAS) for $$MWCVCP_{3}$$ M W C V C P 3 in unit ball graphs when the weight is smooth and weak c-local.

Keywords: PTAS; Connected vertex cover $$P_3$$ P 3; Smooth weights; Weak c-local; Unit ball graph (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10878-015-9937-z

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