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)


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.


Short Path Planar Graph Priority Queue Sparse Graph Adjacency List 
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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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