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A single source shortest path algorithm for graphs with separators

  • K. Mehlhorn
  • B. H. Schmidt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 158)

Abstract

We show how to solve a single source shortest path problem on a planar network in time O(n3/2log n). The algorithm works for arbitrary edge weights (positive and negative) and is based on the planar separator theorem. More generally, the algorithm works in time O(na+blog n + n3a+ nd) on graphs G=(V, E) which have a separator of size na, have at most nb edges and where the separator can be found in time nd.

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References

  1. Bellman R.E. On a Routing Problem Quart. Appl. Math. 16 (1958) pp. 87–90Google Scholar
  2. Dijkstra E.W. A Note on two Problems in Connection with Graphs Num. Math. Vol. 1 (1959) pp. 269–271Google Scholar
  3. Edmonds J., Karp R.M. Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems J. ACM 5 (1962) p. 345Google Scholar
  4. Lipton R., Tarjan R.E. A Separator Theorem for Planar Graphs Waterloo Conference on Theoretical Comp. Science Aug.77 pp. 1–10Google Scholar
  5. Floyd F.W. Algorithm 97: Shortest Path C. ACM 5 (1962) p. 345Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • K. Mehlhorn
    • 1
  • B. H. Schmidt
    • 1
  1. 1.Fachbereich 10 — Angewandte Mathematik und InformatikUniversität des SaarlandesSaarbrückenWest Germany

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