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Fast algorithms for the dominating set problem on permutation graphs

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Abstract

AnO(n log logn) (resp.O(n2 log2 n)) algorithm is presented to solve the minimum cardinality (resp. weight) dominating set problem on permutation graphs, assuming the input is a permutation. The best-known previous algorithm was given by FÄrber and Keil, where they use dynamic programming to get anO(n2 (resp.O(n3)) algorithm. Our improvement is based on the following three factors: (1) an observation on the order among the intermediate terms in the dynamic programming, (2) a new construction formula for the intermediate terms, and (3) efficient data structures for manipulating these terms.

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References

  1. M. J. Atallah, G. K. Manacher, and J. Urrutia, Finding a minimum independent dominating set in a permutation graph,Discrete Appl. Math.,21 (3) (1988), 177–183.

    Google Scholar 

  2. J. L. Bentley, Algorithms for Klee's Rectangle Problems, Unpublished notes, Department of Computer Science, Carnegie-Mellon University, Pittsburgh, PA, 1977.

    Google Scholar 

  3. A. Brandstadt and D. Kratsch, On domination problems for permutation and other graphs,Theoret. Comput. Sci.,54 (1987), 181–198.

    Google Scholar 

  4. M. Farber and J. M. Keil, Domination in permutation graphs,J. Algorithms,6 (1985), 309–321.

    Google Scholar 

  5. J. Spinrad, Transitive orientation inO(n2) time,Proc. 15th Annual ACM Symposium on Theory of Computing, 1983, pp. 457–466.

  6. P. van Emde Boas, Preserving order in a forest in less than logarithmic time and linear space,Inform. Process. Lett.,6 (3) (1977), 80–82.

    Google Scholar 

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Communicated by Takao Asano.

This research was supported in part by the National Science Foundation under Grant CCR-8905415 to Northwestern University.

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Tsai, KH., Hsu, WL. Fast algorithms for the dominating set problem on permutation graphs. Algorithmica 9, 601–614 (1993). https://doi.org/10.1007/BF01190158

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  • DOI: https://doi.org/10.1007/BF01190158

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