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Tight lower bounds for computing shortest paths on proper interval and bipartite permutation graphs

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Parallel Computing Technologies (PaCT 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1277))

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Abstract

Logarithmic time lower bounds for computing the distance between two arbitrary vertices, in a proper interval graph represented by a family of intervals on a real line, and in a bipartite permutation graph represented by a permutation function, on exclusive write PRAM are proved here. The lower bounds are also valid for these classes of graphs represented by adjacency matrices and for their superclasses. Shortest paths on interval and permutation graphs, which, respectively, strictly contain proper interval and bipartite permutation graphs, are known to be computable in logarithmic time on exclusive write PRAM. It follows that the lower bounds derived here are tight.

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References

  1. S. G. Akl and L. Chen. Efficient parallel algorithms on proper circular arc graphs. IEICE Transactions on Information and Systems, E79-D(8):1015–1020, 1996.

    Google Scholar 

  2. D. Z. Chen and D. T. Lee. Solving the all-pair shortest path problem on interval and circular-arc graphs. In Proceedings, Int'l Parallel Processing Symp., pages 224–228, 1994.

    Google Scholar 

  3. L. Chen. Logarithmic time NC algorithms for comparability graphs and circle graphs. In F. Dehne, F. Fiala, and W. W. Koczkodaj, editors, Proceedings, International Conference on Computing and Information, Lecture Notes in Computer Science, Vol. 497, pages 383–394. Springer-Verlag, 1991.

    Google Scholar 

  4. L. Chen. Efficient parallel recognition of some circular arc graphs, I. Algorithmica, 9(3):217–238, March 1993.

    Google Scholar 

  5. L. Chen. Solving the shortest-paths problem on bipartite permutation graphs efficiently. Information Processing Letters, 55(5):259–264, September 1995.

    Google Scholar 

  6. L. Chen and Y. Yesha. Efficient parallel algorithms for bipartite permutation graphs. Networks, 23(1):29–39, January 1993.

    Google Scholar 

  7. S. A. Cook, C. Dwork, and R. Reischuk. Upper and lower time bounds for parallel random access machines without simultaneous writes. SIAM Journal on Computing, 15(1):87–97, 1986.

    Google Scholar 

  8. D. Coppersmith and S. Winograd. Matrix multiplication via arithmetic progressions. Journal of Symbolic Computation, 9:251–280, 1990.

    Google Scholar 

  9. E. W. Dijkstra. A note on two problems in connexion with graphs. Numerische Mathernatik, 1:269–271, 1959.

    Google Scholar 

  10. R. W. Floyd. Algorithm 97: Shortest path. Comm. ACM, 5(6):345, 1962.

    Google Scholar 

  11. M. C. Golumbic. Algorithmic Graph Theory and Perfect Graphs. Computer Science and Applied Mathematics. Academic Press, New York, 1980.

    Google Scholar 

  12. O. H. Ibarra and Q. Zheng. An optimal shortest path parallel algorithm for permutation graphs. J. Parallel & Distributed Computing, 24(1):94–99, 1995.

    Google Scholar 

  13. R. M. Karp and V. Ramachandran. Parallel algorithms for shared-memory machines. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, Vol. A, pages 869–941. North Holland, Amsterdam, 1990.

    Google Scholar 

  14. T. Kashiwabara, S. Masuda, K. Nakajima, and T. Fujisawa. Polynomial time algorithms on circular-arc overlap graphs. Networks, 21(2):195–203, March 1991.

    Google Scholar 

  15. R. Seidel. On the all-pairs-shortest-path problem in unweighted undirected graphs. Journal of Computer and System Sciences, 51(3):400–403, December 1995.

    Google Scholar 

  16. J. Spinrad, A. Brandstädt, and L. Stewart. Bipartite permutation graphs. Discrete Applied Math., 18:279–292, 1987.

    Google Scholar 

  17. T. Takaoka. A new upper bound on the complexity of the all pairs shortest path problem. Information Processing Letters, 43(4):195–199, September 1992.

    Google Scholar 

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Authors and Affiliations

  1. FRL, P. O. Box 18345, 90018, Los Angeles, CA

    Lin Chen

Authors
  1. Lin Chen
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Editor information

Victor Malyshkin

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© 1997 Springer-Verlag Berlin Heidelberg

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Chen, L. (1997). Tight lower bounds for computing shortest paths on proper interval and bipartite permutation graphs. In: Malyshkin, V. (eds) Parallel Computing Technologies. PaCT 1997. Lecture Notes in Computer Science, vol 1277. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63371-5_2

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  • DOI: https://doi.org/10.1007/3-540-63371-5_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63371-6

  • Online ISBN: 978-3-540-69525-7

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