New approximations for minimum-weighted dominating sets and minimum-weighted connected dominating sets on unit disk graphs

  • Authors:

  • Feng Zou;Yuexuan Wang;Xiao-Hua Xu;Xianyue Li;Hongwei Du;Pengjun Wan;Weili Wu

  • Affiliations:

  • Department of Computer Science, University of Texas at Dallas, Richardson, TX 75080, USA;Institute of Theoretical Computer Science, Tsinghua University, Beijing 100084, China;Department of Computer Science, Illinois Institute of Technology, Chicago, IL 60616, USA;School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China;Department of Computer Science, Illinois Institute of Technology, Chicago, IL 60616, USA;Department of Computer Science, Illinois Institute of Technology, Chicago, IL 60616, USA;Department of Computer Science, University of Texas at Dallas, Richardson, TX 75080, USA

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2011

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Abstract

Given a node-weighted graph, the minimum-weighted dominating set (MWDS) problem is to find a minimum-weighted vertex subset such that, for any vertex, it is contained in this subset or it has a neighbor contained in this set. And the minimum-weighted connected dominating set (MWCDS) problem is to find a MWDS such that the graph induced by this subset is connected. In this paper, we study these two problems on a unit disk graph. A (4 +@e)-approximation algorithm for an MWDS based on a dynamic programming algorithm for a Min-Weight Chromatic Disk Cover is presented. Meanwhile, we also propose a (1 +@e)-approximation algorithm for the connecting part by showing a polynomial-time approximation scheme for a Node-Weighted Steiner Tree problem when the given terminal set is c-local and thus obtain a (5 +@e)-approximation algorithm for an MWCDS.