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External Memory Algorithms for Diameter and All-Pairs Shortest-Paths on Sparse Graphs

  • Lars Arge
  • Ulrich Meyer
  • Laura Toma
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3142)

Abstract

We develop I/O-efficient algorithms for diameter and all-pairs shortest-paths (APSP). For general undirected graphs G(V,E) with non-negative edge weights and E/V = o(B/ log V) our approaches are the first to achieve o(V 2) I/Os. We also show that for unweighted undirected graphs, APSP can be solved with just \(O(V \cdot \textrm{sort}(E))\) I/Os. Both our weighted and unweighted approaches require O(V 2) space. For diameter computations we provide I/O-space tradeoffs. Finally, we provide improved results for both diameter and APSP computation on directed planar graphs.

Keywords

Short Path Planar Graph Priority Queue Sparse Graph Adjacency List 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Lars Arge
    • 1
  • Ulrich Meyer
    • 2
  • Laura Toma
    • 3
  1. 1.Department of Computer ScienceDuke UniversityDurhamUSA
  2. 2.Max-Planck-Institut für InformatikSaarbrückenGermany
  3. 3.Department of Computer ScienceBowdoin CollegeBrunswickUSA

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