A dynamization of the All Pairs Least Cost Path Problem

  • Hans Rohnert
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 182)


Given a digraph and a cost function of the edges we update on-line, i.e., between two successive modifications of the cost function, the solution of the All Pairs Least Cost Path Problem (APLCPP). We derive lower and upper bounds for time complexity and show that the gaps between two corresponding bounds are small. Space complexity is quadratic and therefore optimal in our model.


Cost Function Time Complexity Minimum Span Tree Transitive Closure Cost Path 
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5. References

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    S. EVEN/Y. SHILOACH: "An On-Line Edge-Deletion Problem" JACM, vol. 28, no. 1, 1981Google Scholar
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    G.N. FREDERICKSON: "Data Structures for On-Line Updating of Minimum Spanning Trees", CACM, 1983Google Scholar
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    T. IBARAKI/N. KATOH: "On-Line Computation of Transitive Closure of Graphs", Inf.Proc.Let. 16, 1983Google Scholar
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    D.B. JOHNSON:"Efficient Algorithms for Shortest Paths in Sparse Networks, JACM, vol. 24, no. 1, 1977Google Scholar
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    K. MEHLHORN: "Data Structures and Algorithms", Springer-Verlag Berlin-Heidelberg-New York-Tokyo, Vol. I and IIGoogle Scholar
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    V.V. RODIONOV: "The Parametric Problem of Shortest Distances", U.S.S.R. Comput.Math.Math.Phys., 8, 336–343, 1968Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Hans Rohnert
    • 1
  1. 1.Universität SaarbrückenSaarbrückenF.R.G.

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