Average Update Times for Fully-Dynamic All-Pairs Shortest Paths

  • Authors:

  • Tobias Friedrich;Nils Hebbinghaus

  • Affiliations:

  • Max-Planck-Institut für Informatik, Saarbrücken, Germany and International Computer Science Institute, Berkeley, USA;Max-Planck-Institut für Informatik, Saarbrücken, Germany

  • Venue:
  • ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
  • Year:
  • 2008

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Abstract

We study the fully-dynamic all pairs shortest path problem forgraphs with arbitrary non-negative edge weights. It is known fordigraphs that an update of the distance matrix costs$\ensuremath{{\cal \tilde O}}(n^{2.75})$ worst-case time [Thorup,STOC ’05] and $\ensuremath{{\cal \tilde O}}(n^2)$ amortizedtime [Demetrescu and Italiano, J.ACM ’04] where n is thenumber of vertices. We present the first average-case analysis ofthe undirected problem. For a random update we show that theexpected time per update is bounded by O(n4/3 + ε ) for all ε 0.