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European Symposium on Algorithms

ESA 1995: Algorithms — ESA '95 pp 185–198Cite as

On the all-pairs shortest path algorithm of Moffat and Takaoka

  • Session 3. Chair: Giuseppe Italiano
  • Conference paper
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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 979))

Abstract

We review how to solve the all-pairs shortest path problem in a non-negatively weighted digraph with n vertices in expected time O(n 2 log n). This bound is shown to hold with high probability for a wide class of probability distributions on non-negatively weighted digraphs. We also prove that for a large class of probability distributions Ω(n log n) time is necessary with high probability to compute shortest path distances with respect to a single source.

This work is supported by the ESPRIT II Basic Research Actions Program of the EC under contract no. 7141 (project ALCOM II) and the BMFT-project “Softwareökonomie und Softwaresicherheit” ITS 9103

Research supported by a Graduiertenkolleg graduate fellowship of the Deutsche Forschungsgemeinschaft.

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References

  1. P.A. Bloniarz, A shortest-path algorithm with expected time O(n 2 lognlog* n), SIAM J. Comput. 12 (1983) 588–600

    Article  Google Scholar 

  2. E.W. Dijkstra, A note on two problems in connexion with graphs, Numer. Math. 1 (1959) 269–271

    Article  Google Scholar 

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

    Article  Google Scholar 

  4. M.L. Fredman, New bounds on the complexity of the shortest path problem, SIAM J. Comput. 5 (1976) 83–89

    Article  Google Scholar 

  5. M.L. Fredman and R.E. Tarjan, Fibonacci heaps and their uses in improved network optimization algorithms, J. ACM 34 (1987) 596–615

    Article  Google Scholar 

  6. A.M. Frieze and G.R. Grimmett, The shortest-path problem for graphs with random arc-lengths, Discrete Appl. Math. 10 (1985) 57–77

    Google Scholar 

  7. R.L. Graham, D.E. Knuth, and O. Patashnik, Concrete Mathematics (2nd ed.), Addison-Wesley, Reading, MA, 1994

    Google Scholar 

  8. D.R. Karger, D. Koller, and S.J. Phillips, Finding the hidden path: Time bounds for all-pairs shortest paths, SIAM J. Comput. 22 (1993) 1199–1217

    Article  Google Scholar 

  9. C. McDiarmid, On the method of bounded differences, in: J. Siemons (Ed.), Surveys in Combinatorics, 1989 (London Mathematical Society Lecture Notes Series; 141), Cambridge University Press, Cambridge, 1989

    Google Scholar 

  10. A. Moffat and T. Takaoka, An all pairs shortest path algorithm with expected time O(n2 log n), Proc. of the 26th Annual Symposium on Foundations of Computer Science, Portland, OR, 1985, 101–105

    Google Scholar 

  11. A. Moffat and T. Takaoka, An all pairs shortest path algorithm with expected time O(n 2 log n), SIAM J. Comput. 16 (1987) 1023–1031

    Article  Google Scholar 

  12. P.M. Spira, A new algorithm for finding all shortest path in a graph of positive arcs in average time O(n 2 log2 n), SIAM J. Comput. 2 (1973) 28–32

    Article  Google Scholar 

  13. A. Srinivasan, Techniques for probabilistic analysis and randomness-efficient computation, Ph.D. Thesis, Cornell University, Ithaca, NY, Technical Report 93-1378, August 1993

    Google Scholar 

  14. T. Takaoka, A new upper bound on the complexity of the all pairs shortest path problem, Inform. Process. Lett. 43 (1992) 195–199

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Max-Planck-Institut für Informatik, Im Stadtwald, 66123, Saarbrücken, Germany

    Kurt Mehlhorn & Volker Priebe

Authors
  1. Kurt Mehlhorn
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  2. Volker Priebe
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Paul Spirakis

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© 1995 Springer-Verlag Berlin Heidelberg

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Mehlhorn, K., Priebe, V. (1995). On the all-pairs shortest path algorithm of Moffat and Takaoka. In: Spirakis, P. (eds) Algorithms — ESA '95. ESA 1995. Lecture Notes in Computer Science, vol 979. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60313-1_143

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  • DOI: https://doi.org/10.1007/3-540-60313-1_143

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60313-9

  • Online ISBN: 978-3-540-44913-3

  • eBook Packages: Springer Book Archive

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