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Efficient parallel algorithms forr-dominating set andp-center problems on trees

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Abstract

We develop efficient parallel algorithms for ther-dominating set and thep-center problems on trees. On a concurrent-read exclusive-write PRAM, our algorithm for ther-dominating set problem runs inO(logn log logn) time withn processors. The algorithm for thep-center problem runs inO(log2 n log logn) time withn processors.

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References

  1. K. Abrahamson, N. Dadoun, D. G. Kirkpatrick, and T. Przytycka, A Simple Parallel Tree Contraction Algorithm,J. Algorithms,10 (1989), pp. 287–302.

    Article  MATH  MathSciNet  Google Scholar 

  2. A. Borodin and J. E. Hopcroft, Routing, Merging and Sorting on Parallel Models of Computation,J. Comput. System Sci,30 (1985), pp. 130–145.

    Article  MATH  MathSciNet  Google Scholar 

  3. R. Chandrasekaran and A. Tamir, AnO((n log p)2) Algorithm for the Continuous p-Center Problem on a Tree,SIAM J. Algebraic Discrete Methods,1 (4) (1980), pp. 370–375.

    Article  MATH  MathSciNet  Google Scholar 

  4. R. Chandrasekaran and A. Tamir, Polynomially Bounded Algorithms for Locating p-Centers on a Tree,Math. Programming,22 (1982), pp. 304–315.

    Article  MATH  MathSciNet  Google Scholar 

  5. E. Cockayne, S. Goodman, and S. Henetiniemi, A Linear Algorithm for the Domination Number of a Tree,Inform. Process. Lett.,4 (1975), pp. 41–44.

    Article  MATH  Google Scholar 

  6. R. Cole, Parallel Merge Sort,Proc. 27th IEEE Symposium on Foundations of Computer Science, 1986, pp. 511–516.

  7. R. Cole, Slowing Down Sorting Networks to Obtain Faster Sorting Algorithms,J. Assoc. Comput. Mach.,34 (1) (1987), pp. 200–208.

    MathSciNet  Google Scholar 

  8. R. Cole, An Optimally Efficient Selection Algorithm,Inform. Process. Lett.,26 (1988), pp. 295–299.

    Article  MATH  MathSciNet  Google Scholar 

  9. R. Cole and U. Vishkin, The Accelerated Centroid Decomposition Technique for Optimal Parallel Tree Evaluation in Logarithmic Time,Algorithmica,3 (1988), pp. 329–346.

    Article  MATH  MathSciNet  Google Scholar 

  10. D. M. Dearing and R. L. Francis, A Minimax Location Problem on a Network,Transportation Sci,8 (1974), pp. 333–343.

    MathSciNet  Google Scholar 

  11. G. N. Frederickson and D. B. Johnson, Finding kth Path and p-Centers by Generating and Searching Good Data Structures,J. Algorithms,4 (1983), pp. 61–80.

    Article  MATH  MathSciNet  Google Scholar 

  12. A. G. Goldman, Minimax Location of a Facility in an Undirected Tree Graph,Transportation Sci,6 (1972), pp. 407–418.

    MathSciNet  Google Scholar 

  13. S. L. Hakimi, Optimum Locations of Switching Centers and Absolute Centers and Medians of a Graph,Oper. Res.,12 (1964), pp. 450–459.

    MATH  Google Scholar 

  14. S. L. Hakimi, Optimal Distribution of Switching Centers in a Communication Network and Some Related Graph Theoretic Problems,Oper. Res.,13 (1965), pp. 462–475.

    Article  MATH  MathSciNet  Google Scholar 

  15. G. Y. Handler, Finding Two Centers of a Tree, the Continuous Case,Transportation Sci,12 (1978), pp. 93–106.

    MathSciNet  Google Scholar 

  16. X. He and Y. Yesha, Binary Tree Algebraic Computation and Parallel Algorithms for Simple Graphs,J. Algorithms,9 (1988), pp. 92–113.

    Article  MATH  MathSciNet  Google Scholar 

  17. O. Kariv and S. L. Hakimi, An Algorithmic Approach on Network Location Problems I: the p-Centers,SIAM J. Appl. Math.,37 (3) (1979), pp. 513–538.

    Article  MATH  MathSciNet  Google Scholar 

  18. N. Megiddo, A. Tamir, E. Zemel, and R. Chandrasekaran, AnO(n log2 n) Algorithm for the feth Longest Path in a Tree with Applications to Location Problems,SIAM J. Comput.,10 (2) (1981), pp. 328–337.

    Article  MATH  MathSciNet  Google Scholar 

  19. N. Megiddo and A. Tamir, New Results on the Complexity of P-Center Problems,SIAM J. Comput,12 (4) (1983), pp. 751–759.

    Article  MATH  MathSciNet  Google Scholar 

  20. G. L. Miller and J. Reif, Parallel Tree Contraction and Its Applications,Proc. 26th IEEE Symposium on Foundations of Computer Science, 1985, pp. 478–489.

  21. P. J. Slater, R-Domination in Graphs,J. Assoc. Comput. Mach.,23 (3) (1976), pp. 446–450.

    MATH  MathSciNet  Google Scholar 

  22. R. E. Tarjan and U. Vishkin, Finding Biconnected Components and Computing Tree Functions in Logarithmic Parallel Time,SIAM J. Comput.,14 (4) (1985), pp. 862–874.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, State University of New York at Buffalo, 14260, Buffalo, NY, USA

    Xin He

  2. Department of Computer and Information Science, Ohio State University, 43210, Columbus, OH, USA

    Yaacov Yesha

Authors
  1. Xin He
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  2. Yaacov Yesha
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Additional information

Communicated by Richard M. Karp.

Xin He was supported in part by an Ohio State University Presidential Fellowship, and by the Office of Research and Graduate Studies of Ohio State University. Yaacov Yesha was supported in part by the National Science Foundation under Grant No. DCR-8606366.

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He, X., Yesha, Y. Efficient parallel algorithms forr-dominating set andp-center problems on trees. Algorithmica 5, 129–145 (1990). https://doi.org/10.1007/BF01840381

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  • DOI: https://doi.org/10.1007/BF01840381

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