Skip to main content
SpringerLink
Log in

Shortest paths in random weighted graphs

  • Session 4A: Graph Algorithms
  • Conference paper
  • First Online:
Book cover Computing and Combinatorics (COCOON 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 959))

Included in the following conference series:

Abstract

We consider the probability distribution of the cost of shortest paths and the diameter in a complete, weighted digraph with non-negative random edge costs. Asymptotic results as the number of nodes goes to infinity are developed and applied to extend several probabilistic shortest path algorithms to edge cost distributions having a general Taylor's series at zero edge cost.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. K. Ahuja, K. Mehlhorn, J. B. Orlin, and R. E. Tarjan: Faster Algorithms for the Shortest Path Problem. Technical Report CS-TR-154-88, Department of Computer Science, Princeton University. (1988)

    Google Scholar 

  2. P.A. Bloniarz: A shortest-path algorithm with expected time O(n 2 log n log* n). Technical Report 80-3, Dept. of Computer Science, State Univ. of New York at Albany. (1980)

    Google Scholar 

  3. M. L. Fredman and R. E. Tarjan: Fibonacci heaps and their uses in improved network optimization algorithms. J. Assoc. Comput. Mach. 34 (1987) 596–615

    Google Scholar 

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

    Article  Google Scholar 

  5. G. Gallo and S. Pallottino: Shortest path algorithms. Annals of Oper. Res. 13 (1988) 3–79

    Google Scholar 

  6. A. V. Goldberg: Scaling algorithms for the shortest paths problem. Proc. 4th ACM-SIAM symposium of Discrete Algorithms. (1993) 222–231

    Google Scholar 

  7. Refael Hassin and Eitan Zemel: On shortest paths in graphs with random weights. Math. of Oper. Res. 10 (1985) 557–564

    Google Scholar 

  8. P. Spira: A new algorithm for finding all shortest paths in a graph of positive edges in average time O(n 2log2 n). SIAM J. Comput. 2 (1973) 28–32

    Article  Google Scholar 

  9. Scott K. Walley, Harry H. Tan, and Audrey M. Viterbi. Shortest path cost distribution in random graphs with positive integer edge costs. Proc. of IEEE INFO-COM'93. (1993) 1023–1032

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of California, Irvine, 92717, Irvine, CA, USA

    Scott K. Walley & Harry H. Tan

Authors
  1. Scott K. Walley
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Harry H. Tan
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Ding-Zhu Du Ming Li

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Walley, S.K., Tan, H.H. (1995). Shortest paths in random weighted graphs. In: Du, DZ., Li, M. (eds) Computing and Combinatorics. COCOON 1995. Lecture Notes in Computer Science, vol 959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030835

Download citation

  • DOI: https://doi.org/10.1007/BFb0030835

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60216-3

  • Online ISBN: 978-3-540-44733-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation