An Optimal Algorithm for Finding the Minimum Cardinality Dominating Set on Permutation Graphs

  • H. S. Chao
  • F. R. Hsu
  • R. C. T. Lee
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1449)


A dominating set D of an undirected graph G is a set of vertices such that every vertex not in D is adjacent to at least one vertex in D. Given a undirected graph G, the minimal cardinality dominating set problem is to find a dominating set of G with minimum number of vertices. The minimal cardinality dominating set problem is NP-hard for general graphs. For permutation graphs, the best-known algorithm ran in O(n log log n) time, where n is the number of vertices. In this paper, we present an optimal O(n) algorithm.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • H. S. Chao
    • 1
  • F. R. Hsu
    • 2
  • R. C. T. Lee
    • 3
  1. 1.Dept. of Computer ScienceNational Tsing Hua UniversityHsinchuTaiwan
  2. 2.Department of AccountingProvidence UniversityShalu, Taichung HsienTaiwan
  3. 3.Office of the PresidentProvidence UniversityShalu, Taichung HsienTaiwan

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