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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)

Abstract

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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References

  1. 1.
    M. Farber and J. M. Keil. Domination in permutation graphs. Journal of Algorithms, 6:309–321, 1985.zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    M. R. Garey and D. S. Johnson. Computers and Intractability, A Guide to the Theory of NP-Completeness. W. H. Freeman, San Francisco, CA, 1979.zbMATHGoogle Scholar
  3. 3.
    M. C. Golumbic. Algorithmic Graph Theory and Perfect Graphs. Academic Press, New York, 1980.zbMATHGoogle Scholar
  4. 4.
    Y. D. Liang, C. Rhee, S. K. Dhall, and S. Lakshmivarahan. A new approach for the domination problem on permutation graphs. Information Processing Letters, 37:219–224, 1991.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    C. Rhee, Y. D. Liang, S. K. Dhall, and S. Lakshmivarahan. An O(m+n) algorithm for finding minimum weight dominating set in permutation graphs. SIAM Journal on Computing, 25(2):404–419, 1996.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    K. H. Tsai and W. L. Hsu. Fast algorithms for the dominating set problem on permutation graphs. Algorithmica, 9:601–614, 1993.zbMATHCrossRefMathSciNetGoogle Scholar

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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