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International Symposium on Algorithms and Computation

ISAAC 2002: Algorithms and Computation pp 32–43Cite as

On the Comparison-Addition Complexity of All-Pairs Shortest Paths

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2518))

Abstract

We present an all-pairs shortest path algorithm for arbitrary graphs that performs O(mn log α) comparison and addition operations, where m and n are the number of edges and vertices, resp., and α = α(m, n) is Tarjan’s inverse-Ackermann function. Our algorithm eliminates the sorting bottleneck inherent in approaches based on Dijkstra’s algorithm, and for graphs with O(n) edges our algorithm is within a tiny O(log α) factor of optimal. The algorithm can be implemented to run in polynomial time (though it is not a pleasing polynomial). We leave open the problem of providing an efficient implementation.

This work was supported by Texas Advanced Research Program Grant 003658-0029-1999, NSF Grant CCR-9988160, and an MCD Graduate Fellowship.

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Author information

Authors and Affiliations

  1. Department of Computer Sciences, The University of Texas at Austin, Austin, TX, 78712

    Seth Pettie

Authors
  1. Seth Pettie
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Editor information

Editors and Affiliations

  1. School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario, Canada, K1S 5B6

    Prosenjit Bose  & Pat Morin  & 

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© 2002 Springer-Verlag Berlin Heidelberg

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Pettie, S. (2002). On the Comparison-Addition Complexity of All-Pairs Shortest Paths. In: Bose, P., Morin, P. (eds) Algorithms and Computation. ISAAC 2002. Lecture Notes in Computer Science, vol 2518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36136-7_4

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  • DOI: https://doi.org/10.1007/3-540-36136-7_4

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00142-3

  • Online ISBN: 978-3-540-36136-7

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