MPI-INF/SWS Research Reports 1991-2021

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Improved algorithms for all-pairs approximate shortest paths in weighted graphs

Baswana, Surender and Telikepalli, Kavitha

September 2005, 26 pages.

Status: available - back from printing

The all-pairs approximate shortest-paths problem is an interesting variant of the classical all-pairs shortest-paths problem in graphs. The problem aims at building a data-structure for a given graph with the following two features. Firstly, for any two vertices, it should report an {\emph{approximate}} shortest path between them, that is, a path which is longer than the shortest path by some {\emph{small}} factor. Secondly, the data-structure should require less preprocessing time (strictly sub-cubic) and occupy optimal space (sub-quadratic), at the cost of this approximation. In this paper, we present algorithms for computing all-pairs approximate shortest paths in a weighted undirected graph. These algorithms significantly improve the existing results for this problem.

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  AUTHOR = {Baswana, Surender and Telikepalli, Kavitha},
  TITLE = {Improved algorithms for all-pairs approximate shortest paths in weighted graphs},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Stuhlsatzenhausweg 85, 66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-2005-1-003},
  MONTH = {September},
  YEAR = {2005},
  ISSN = {0946-011X},