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Annual Asian Computing Science Conference

ASIAN 1998: Advances in Computing Science ASIAN 98 pp 113–124Cite as

An Optimal Parallel Algorithm for the Perfect Dominating Set Problem on Distance-Hereditary Graphs

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1538))

Abstract

In the literature, there are quite a few sequential and parallel algorithms for solving problems on distance-hereditary graphs. With an n-vertex distance-hereditary graph G, we show that the perfect dominating set problem on G can be solved in O(log2 n) time using O(n+m) procesors on a CREW PRAM

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References

  1. K. Abrahamson, N. Dadoun, D. G. Kirkpatrick, and T. Przytycka, A simple parallel tree contraction algorithm. Journal of Algorithms., 10, pp. 287–302, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  2. H. J. Bandelt and H. M. Mulder. Distance-hereditary graphs. Journal of Combinatorial Theory Series B, 41(1):182–208, Augest 1989.

    Google Scholar 

  3. C. Berge. Graphs and hypergraphs. North-Holland, Amsterdam, 1973.

    MATH  Google Scholar 

  4. N. Biggs. Perfect codes in graphs. J. Combin. Theory Ser. B, 15:289–296, 1973.

    Article  MATH  MathSciNet  Google Scholar 

  5. A. Brandstädt and F. F. Dragan, A linear time algorithm for connected γ-domination and Steiner tree on distance-hereditary graphs, Networks, 31:177–182, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  6. M. S. Chang and Y. C. Liu. Polynomial algorithm for the weighted perfect domination problems on chordal graphs and split graphs. Information Processing Letters, 48:205–210, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  7. G. J. Chang, C. Pandu Rangan, and S. R. Coorg. Weighted independent perfect domination on cocomparability graphs. Discrete Applied Mathematics, 63:215–222, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  8. M. S. Chang, S. Y. Hsieh, and G. H. Chen. Dynamic Programming on Distance-Hereditary Graphs. Proceedings of 7th International Symposium on Algorithms and Computation, ISAAC’97, LNCS 1350, pp. 344–353.

    Google Scholar 

  9. E. Dahlhaus, “Optimal (parallel) algorithms for the all-to-all vertices distance problem for certain graph classes,” Lecture notes in computer science 726, pp. 60–69.

    Google Scholar 

  10. E. Dahlhaus. Efficient parallel recognition algorithms of cographs and distance-hereditary graphs. Discrete applied mathematics, 57(1):29–44, February 1995.

    Google Scholar 

  11. A. D’atri and M. Moscarini. Distance-hereditary graphs, steiner trees, and connected domination. SIAM Journal on Computing, 17(3):521–538, June, 1988.

    Google Scholar 

  12. F. F. Dragan, Dominating cliques in distance-hereditary graphs, Algorithm Theory-SWAT’94 “4th Scandinavian Workshop on Algorithm Theory, LNCS 824, Springer, Berlin, pp. 370–381, 1994.

    Google Scholar 

  13. M. C. Golumbic. Algorithmic graph theory and perfect graphs, Academic press, New York, 1980.

    MATH  Google Scholar 

  14. P. L. Hammer and F. Maffray. Complete separable graphs. Discrete applied mathematics, 27(1):85–99, May 1990.

    Google Scholar 

  15. X. He. Efficient parallel algorithms for solving some tree problems. Proc. 24th Allerton Conference on Communication, Control, and Computing, 777–786, 1986.

    Google Scholar 

  16. X. He. Efficient parallel algorithms for series-parallel graphs. Journal of Algorithms, 12:409–430, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  17. X. He and Y. Yesha. Binary tree algebraic computation and parallel algorithms for simple graphs. Journal of Algorithms, 9:92–113, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  18. E. Howorka. A characterization of distance-hereditary graphs. Quarterly Journal of Mathematics (Oxford), 28(2):417–420. 1977.

    Article  MATH  MathSciNet  Google Scholar 

  19. S.-y. Hsieh, C. W. Ho, T.-s. Hsu, M. T. Ko, and G. H. Chen. Efficient parallel algorithms on distance-hereditary graphs. Parallel Processing Letters, to appear. A preliminary version of this paper is in Proceedings of the International Conference on Parallel Processing, pp. 20–23, 1997.

    Google Scholar 

  20. S.-y. Hsieh, Parallel decomposition of Distance-Hereditary Graphs with its application. Manuscript, 1998.

    Google Scholar 

  21. S.-y. Hsieh, C. W. Ho, T.-s. Hsu, M. T. Ko, and G. H. Chen. A new simple tree contraction scheme and its application on distance-hereditary graphs. Proceedings of Irregular’98, LNCS, Springer-Verlag, to appear.

    Google Scholar 

  22. S.-y. Hsieh, C. W. Ho, T.-s. Hsu, M. T. Ko, and G. H. Chen. Characterization of efficiently solvable problems on distance-hereditary Graphs. Proceedings of 8th International Symposium on Algorithms and Computation, ISAAC’98, Springer-Verlag, to appear.

    Google Scholar 

  23. M. Livingston and Q. F. Stout. Perfect dominating sets. Congr. Numer., 79:187–203, 1990.

    MATH  MathSciNet  Google Scholar 

  24. Falk Nicolai. Hamiltonian problems on distance-hereditary graphs. Technique report, Gerhard-Mercator University, Germany, 1994.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan

    Sun-Yuan Hsieh & Gen-Huey Chen

  2. Department of Computer Science and Information Engineering, National Central University, Chung-Li, Taiwan

    Chin-Wen Ho

Authors
  1. Sun-Yuan Hsieh
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  2. Gen-Huey Chen
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  3. Chin-Wen Ho
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Editor information

Editors and Affiliations

  1. College of Science and Technology, National Chi-Nan University, Puli, Nantou, Taiwan

    Jieh Hsiang

  2. Research Institute for Mathematical Sciences, Kyoto University, Sakyo-ku, Kyoto, 606-8502, Japan

    Atsushi Ohori

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© 1998 Springer-Verlag Berlin Heidelberg

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Hsieh, SY., Chen, GH., Ho, CW. (1998). An Optimal Parallel Algorithm for the Perfect Dominating Set Problem on Distance-Hereditary Graphs. In: Hsiang, J., Ohori, A. (eds) Advances in Computing Science ASIAN 98. ASIAN 1998. Lecture Notes in Computer Science, vol 1538. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49366-2_10

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  • DOI: https://doi.org/10.1007/3-540-49366-2_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65388-2

  • Online ISBN: 978-3-540-49366-2

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