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All-Pairs Shortest Paths Computation in the BSP Model

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Automata, Languages and Programming (ICALP 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2076))

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Abstract

The model of bulk-synchronous parallel (BSP) computation is an emerging paradigm of general-purpose parallel computing. We propose a new p-processor BSP algorithm for the all-pairs shortest paths problem in a weighted directed dense graph. In contrast with the general algebraic path algorithm, which performs O(p 1/2) to O(p 2/3) global synchronisation steps, our new algorithm only requires O(log p) synchronisation steps.

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References

  1. A. Aggarwal, A. K. Chandra, and M. Snir. Communication complexity of PRAMs. Theoretical Computer Science, 71(1):3–28, March 1990.

    Article  MATH  MathSciNet  Google Scholar 

  2. N. Alon, Z. Galil, and O. Margalit. On the exponent of the all pairs shortest path problem. Journal of Computer and System Sciences, 54(2):255–262, April 1997.

    Article  MATH  MathSciNet  Google Scholar 

  3. B. Carré. Graphs and Networks. Oxford Applied Mathematics and Computer Science Series. Clarendon Press, 1979.

    Google Scholar 

  4. D. Coppersmith and S. Winograd. Matrix multiplication via arithmetic progressions. Journal of Symbolic Computation, 9(3):251–280, March 1990.

    Article  MATH  MathSciNet  Google Scholar 

  5. T. H. Cormen, C. E. Leiserson, and R. L. Rivest. Introduction to Algorithms. The MIT Electrical Engineering and Computer Science Series. The MIT Press and McGraw-Hill, 1990.

    Google Scholar 

  6. E. W. Dijkstra. A note on two problems in connection with graphs. Numerische Mathematik, 1:269–271, 1959.

    Article  MATH  MathSciNet  Google Scholar 

  7. I. Foster. Designing and Building Parallel Programs. Addison-Wesley, 1995.

    Google Scholar 

  8. M. Gondran and M. Minoux. Graphs and Algorithms. Wiley—Interscience Series in Discrete Mathematics. John Wiley & Sons, 1984.

    Google Scholar 

  9. M. Gondran and M. Minoux. Linear algebra in dioids: A survey of recent results. Annals of Discrete Mathematics, 19:147–164, 1984.

    MathSciNet  Google Scholar 

  10. D. B. Johnson. Efficient algorithms for shortest paths in sparse networks. Journal of the ACM, 24(1):1–13, January 1977.

    Article  MATH  Google Scholar 

  11. W. F. McColl. Scalable computing. In J. van Leeuwen, editor, Computer Science Today: Recent Trends and Developments, volume 1000 of Lecture Notes in Computer Science, pages 46–61. Springer-Verlag, 1995.

    Google Scholar 

  12. W. F. McColl. A BSP realisation of Strassen’s algorithm. In M. Kara, J. R. Davy, D. Goodeve, and J. Nash, editors, Abstract Machine Models for Parallel and Distributed Computing, pages 43–46. IOS Press, 1996.

    Google Scholar 

  13. W. F. McColl. Universal computing. In L. Bougé et al., editors, Proceedings of Euro-Par’ 96 (Part I), volume 1123 of Lecture Notes in Computer Science, pages 25–36. Springer-Verlag, 1996.

    Google Scholar 

  14. G. Rote. Path problems in graphs. Computing Supplementum, 7:155–189, 1990.

    MathSciNet  Google Scholar 

  15. T. Takaoka. Subcubic cost algorithms for the all pairs shortest path problem. Algorithmica, 20:309–318, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  16. A. Tiskin. The bulk-synchronous parallel random access machine. Theoretical Computer Science, 196(1-2):109–130, April 1998.

    Article  MATH  MathSciNet  Google Scholar 

  17. A. Tiskin. Bulk-synchronous parallel Gaussian elimination. In N. N. Vasil’ev and A. M. Vershik, editors, Representation Theory, Dynamical Systems, Combinatorial and Algorithmic Methods (Part 4), volume 258 of Zapiski Nauchnykh Seminarov POMI. Russian Academy of Sciences, 1999. Also to appear in Journal of Mathematical Sciences.

    Google Scholar 

  18. L. G. Valiant. A bridging model for parallel computation. Communications of the ACM, 33(8):103–111, August 1990.

    Article  Google Scholar 

  19. U. Zimmermann. Linear and Combinatorial Optimization in Ordered Algebraic Structures, volume 10 of Annals of Discrete Mathematics. North-Holland, 1981.

    Google Scholar 

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Authors
  1. Alexandre Tiskin
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Editors and Affiliations

  1. Departament de Llenguatges i Sistemes Informátics, Univ. Politècnica de Catalunya, C/Jordi Girona Salgado 1-3, 08034, Barcelona, Spain

    Fernando Orejas

  2. Computer Technology Institute (CTI), University of Patras, 61 Riga Feraiou street, 26221, Patras, Greece

    Paul G. Spirakis

  3. Institute of Information and Computing Sciences, Utrecht University, Padualaan 14, 3584, CH, Utrecht, The Netherlands

    Jan van Leeuwen

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© 2001 Springer-Verlag Berlin Heidelberg

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Tiskin, A. (2001). All-Pairs Shortest Paths Computation in the BSP Model. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds) Automata, Languages and Programming. ICALP 2001. Lecture Notes in Computer Science, vol 2076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48224-5_15

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  • DOI: https://doi.org/10.1007/3-540-48224-5_15

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42287-7

  • Online ISBN: 978-3-540-48224-6

  • eBook Packages: Springer Book Archive

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