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A PTAS for Weak Minimum Routing Cost Connected Dominating Set of Unit Disk Graph

In: Optimization, Simulation, and Control

Author

Listed:
  • Qinghai Liu

    (Xinjiang University)

  • Zhao Zhang

    (Xinjiang University)

  • Yanmei Hong

    (Shanghai Univiersity)

  • Weili Wu

    (University of Texas at Dallas)

  • Ding-Zhu Du

    (University of Texas at Dallas)

Abstract

Considering the virtual backbone problem of wireless sensor networks with the shortest path constraint, the problem can be modeled as finding a minimum routing cost connected dominating set (MOC-CDS) in the graph. In this chapter, we study a variation of the MOC-CDS problem. Let k be a fixed positive integer. For any two vertices u, v of G and a vertex subset $$S \subseteq V (G)$$ , denote ℓ S (u, v) the length of the shortest (u, v)-path in G all whose intermediate vertices are in S and define $$g(u,v) = \left \{\begin{array}{@{}l@{\quad }l@{}} d(u,v) + 4, \quad &\mbox{ if }d(u,v) \leq k + 1; \\ (1 + \frac{4} {k})d(u,v) + 6,\quad &\mbox{ if }d(u,v) > k + 1. \end{array} \right.$$ The g-MOC-CDS problem asks for a subset S with the minimum cardinality such that S is a connected dominating set of G and $${\mathcal{l}}_{S}(u,v) \leq g(u,v)$$ for any pair of vertices (u, v) of G. Clearly, g-MOC-CDS can serve as a virtual backbone of the network such that the routing cost is not increased too much. In this chapter, we give a PTAS for the g-MOC-CDS problem on unit disk graphs.

Suggested Citation

  • Qinghai Liu & Zhao Zhang & Yanmei Hong & Weili Wu & Ding-Zhu Du, 2013. "A PTAS for Weak Minimum Routing Cost Connected Dominating Set of Unit Disk Graph," Springer Optimization and Its Applications, in: Altannar Chinchuluun & Panos M. Pardalos & Rentsen Enkhbat & E. N. Pistikopoulos (ed.), Optimization, Simulation, and Control, edition 127, pages 131-142, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-5131-0_9
    DOI: 10.1007/978-1-4614-5131-0_9
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