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External Memory Algorithms for Diameter and AllPairs ShortestPaths on Sparse Graphs

Summary: External Memory Algorithms for Diameter and
All­Pairs Shortest­Paths on Sparse Graphs
Lars Arge 1,# , Ulrich Meyer 2,## , and Laura Toma 3,# # #
1 Department of Computer Science, Duke University, Durham, NC 27708, USA.
2 Max­Planck­Institut f˜ur Informatik, 66123 Saarbr˜ucken, Germany.
3 Department of Computer Science, Bowdoin College, Brunswick, ME 04011, USA.
Abstract. We develop I/O­e#cient algorithms for diameter and all­
pairs shortest­paths (APSP). For general undirected graphs G(V, E) with
non­negative 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 undi­
rected graphs, APSP can be solved with just O(V · sort(E)) I/Os. Both
our weighted and unweighted approaches require O(V 2 ) space. For di­
ameter computations we provide I/O­space tradeo#s. Finally, we provide
improved results for both diameter and APSP computation on directed
planar graphs.
1 Introduction
Computing shortest paths and diameter of a graph are fundamental problems in
algorithmic graph theory. For example, research in web modeling uses shortest
path and diameter computations as primitive routines for investigating the struc­
ture of the web. Further applications often appear in Geographic Information


Source: Arge, Lars - Department of Computer Science, Aarhus Universitet


Collections: Computer Technologies and Information Sciences