Approximation algorithms for 2-source minimum routing cost k-tree problems

  • Authors:

  • Yen Hung Chen;Gwo-Liang Liao;Chuan Yi Tang

  • Affiliations:

  • Department of Information Science and Management Systems, National Taitung University, Taitung, Taiwan, R.O.C.;Department of Information Science and Management Systems, National Taitung University, Taitung, Taiwan, R.O.C.;Department of Computer Science, National Tsing Hua University, Hsinchu, Taiwan, R.O.C.

  • Venue:
  • ICCSA'07 Proceedings of the 2007 international conference on Computational science and its applications - Volume Part III
  • Year:
  • 2007

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Abstract

In this paper, we investigate some k-tree problems of graphs with given two sources. Let G = (V, E, ω) be an undirected graph with nonnegative edge lengths and two sources s1, s2∈V. The first problem is the 2-source minimum routing cost k-tree (2-kMRCT) problem, in which we want to find a tree T= (VT, ET) spanning kvertices such that the total distance from all vertex in VT to the two sources is minimized, i.e., we want to minimize Σv∈VT{dT(s1, v) + dT(s2, v)}, in which dT(s, v) is the length of the path between s and v on T. The second problem is the 2- source bottleneck source routing cost k-tree (2-kBSRT) problem, in which the objective function is the maximum total distance from any source to all vertices in VT, i.e., maxs∈(s1, s2){Σv∈VT dT(s, v)}. The third problem is the 2-source bottleneck vertex routing cost k-tree (2-kBVRT) problem, in which the objective function is the maximum total distance from any vertex in VT to the two sources, i.e., maxv∈VT{dT(s1, v) + dT(s2, v)}. In this paper, we present polynomial time approximation schemes (PTASs) for the 2-kMRCT and 2-kBVRT problems. For the 2-kBSRT problem, we give a (2 + Ɛ)-approximation algorithm for any Ɛ 0.