On construction of quality fault-tolerant virtual backbone in wireless networks

  • Authors:

  • Wei Wang;Donghyun Kim;Min Kyung An;Wei Gao;Xianyue Li;Zhao Zhang;Weili Wu

  • Affiliations:

  • Department of Mathematics, Xi'an Jiaotong University, Xi'an, China;Department of Mathematics and Computer Science, North Carolina Central University, Durham, NC;Department of Computer Science, University of Texas at Dallas, Richardson, TX;Department of Mathematics, Xi'an Jiaotong University, Xi'an, China;School of Mathematics and Statistics, Lanzhou University, Lanzhou, China;College of Mathematics and System Sciences, Xinjiang University, Urumqi, China;Department of Computer Science, University of Texas at Dallas, Richardson, TX

  • Venue:
  • IEEE/ACM Transactions on Networking (TON)
  • Year:
  • 2013

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Abstract

In this paper, we study the problem of computing quality fault-tolerant virtual backbone in homogeneous wireless network, which is defined as the k-connected m-dominating set problem in a unit disk graph. This problem is NP-hard, and thus many efforts have been made to find a constant factor approximation algorithm for it, but never succeeded so far with arbitrary k ≥ 3 and m ≥ 1 pair. We propose a new strategy for computing a smaller-size 3-connected m-dominating set in a unit disk graph with any m ≥ 1. We show the approximation ratio of our algorithm is constant and its running time is polynomial. We also conduct a simulation to examine the average performance of our algorithm. Our result implies that while there exists a constant factor approximation algorithm for the k-connected m-dominating set problem with arbitrary k ≤ 3 and m ≥ 1 pair, the k-connected m-dominating set problem is still open with k 3.