Fully-Dynamic All-Pairs Shortest Paths: Faster and Allowing Negative Cycles

  • Mikkel Thorup
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3111)

Abstract

We present a solution to the fully-dynamic all pairs shortest path problem for a directed graph with arbitrary weights allowing negative cycles. We support each vertex update in \(O(n^2({\rm log} n + {\rm log^2}(\overline{m}/n)))\) amortized time. Here, n is the number vertices, m the number of edges and \(\overline{m} = n + m\). A vertex update inserts or deletes a vertex with all incident edges, and we update a complete distance matrix accordingly. The algorithm runs on a comparison-addition based pointer-machine.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Mikkel Thorup
    • 1
  1. 1.AT&T Labs–Research, Shannon LaboratoryFlorham ParkUSA

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