Balancing minimum spanning trees and multiple-source minimum routing cost spanning trees on metric graphs

  • Authors:

  • Chung-Ming Lin;Yin Te Tsai;Chuan Yi Tang

  • Affiliations:

  • Department of Computer Science, National Tsing-Hua University, Taiwan, ROC;Department of Computer Science and Communication Engineering, Providence University, Taiwan, ROC;Department of Computer Science, National Tsing-Hua University, Taiwan, ROC

  • Venue:
  • Information Processing Letters
  • Year:
  • 2006

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Abstract

Both the building cost and the multiple-source routing cost are important considerations in construction of a network system. A spanning tree with minimum building cost among all spanning trees is called a minimum spanning tree (MST), and a spanning tree with minimum k-source routing cost among all spanning trees is called a k-source minimum routing cost spanning tree (k-MRCT). This paper proposes an algorithm to construct a spanning tree T for a metric graph G with a source vertex set S such that the building cost of T is at most 1 + 2/(α - 1) times of that of an MST of G, and the k-source routing cost of T is at most α(1+2(k-1)(n - 2)/k(n + k - 2)) times of that of a k-MRCT of G with respect to S, where α 1, k = |S| and n is the number of vertices of G.