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On Dynamic Shortest Paths Problems

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Algorithms – ESA 2004 (ESA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3221))

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Abstract

We obtain the following results related to dynamic versions of the shortest-paths problem:

(i). Reductions that show that the incremental and decremental single-source shortest-paths problems, for weighted directed or undirected graphs, are, in a strong sense, at least as hard as the static all-pairs shortest-paths problem. We also obtain slightly weaker results for the corresponding unweighted problems.

(ii). A randomized fully-dynamic algorithm for the all-pairs shortest-paths problem in directed unweighted graphs with an amortized update time of \(\tilde{O}(m\sqrt n)\) and a worst case query time is O(n 3/4).

(iii). A deterministic O(n 2log n) time algorithm for constructing a (log n)-spanner with O(n) edges for any weighted undirected graph on n vertices. The algorithm uses a simple algorithm for incrementally maintaining single-source shortest-paths tree up to a given distance.

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Authors and Affiliations

  1. School of Computer Science, Tel Aviv University, Tel Aviv, 69978, Israel

    Liam Roditty & Uri Zwick

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  1. Liam Roditty
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  2. Uri Zwick
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Editors and Affiliations

  1. University of Freiburg, Georges Köhler Allee 79, 79110, Freiburg, Germany

    Susanne Albers

  2. Department of Computer Science, King’s College, WC2R 2LS, London, UK

    Tomasz Radzik

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© 2004 Springer-Verlag Berlin Heidelberg

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Roditty, L., Zwick, U. (2004). On Dynamic Shortest Paths Problems. In: Albers, S., Radzik, T. (eds) Algorithms – ESA 2004. ESA 2004. Lecture Notes in Computer Science, vol 3221. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30140-0_52

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  • DOI: https://doi.org/10.1007/978-3-540-30140-0_52

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23025-0

  • Online ISBN: 978-3-540-30140-0

  • eBook Packages: Springer Book Archive

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