A greedy approximation for minimum connected dominating sets

  • Authors:

  • Lu Ruan;Hongwei Du;Xiaohua Jia;Weili Wu;Yingshu Li;Ker-I Ko

  • Affiliations:

  • Department of Computer Science, Iowa State University, Ames, IA;Department of Computer Science, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong;Department of Computer Science, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong;Department of Computer Science, University of Texas at Dellas, Richardson, TX;Department of Computer Science, State University of Minnesota, Minneapolis, MN;Department of Computer Science, State University of New York, Stony Brook, NY

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2004

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Abstract

Given a graph, a connected dominating set is a subset of vertices such that every vertex is either in the subset or adjacent to a vertex in the subset and the subgraph induced by the subset is connected. A minimum connected dominating set is such a vertex subset with minimum cardinality. In this paper, we present a new one-step greedy approximation with performance ratio ln δ + 2 where δ is the maximum degree in the input graph. The interesting aspect is that the greedy potential function of this algorithm is not supmodular while all previously known one-step greedy algorithms with similar performance have supmodular potential functions.