Two Constant Approximation Algorithms for Node-Weighted Steiner Tree in Unit Disk Graphs

  • Authors:

  • Feng Zou;Xianyue Li;Donghyun Kim;Weili Wu

  • Affiliations:

  • Department of Computer Science, University of Texas at Dallas, Richardson 75080;School of Mathematics and Statistics, Lanzhou University, Lanzhou, P.R. China 730000;Department of Computer Science, University of Texas at Dallas, Richardson 75080;Department of Computer Science, University of Texas at Dallas, Richardson 75080

  • Venue:
  • COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
  • Year:
  • 2008

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Abstract

Given a graph G= (V,E) with node weight w: V驴R+and a subset S驴 V, find a minimum total weight tree interconnecting all nodes in S. This is the node-weighted Steiner tree problem which will be studied in this paper. In general, this problem is NP-hard and cannot be approximated by a polynomial time algorithm with performance ratio aln nfor any 0 aNP驴 DTIME(nO(logn)), where nis the number of nodes in s. In this paper, we show that for unit disk graph, the problem is still NP-hard, however it has polynomial time constant approximation. We will present a 4-approximation and a 2.5ρ-approximation where ρis the best known performance ratio for polynomial time approximation of classical Steiner minimum tree problem in graphs. As a corollary, we obtain that there is polynomial time (9.875+驴)-approximation algorithm for minimum weight connected dominating set in unit disk graphs.