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

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons44080

Baswana,  Surender
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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MPI-I-2005-1-003.ps
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Citation

Baswana, S., & Telikepalli, K.(2005). Improved algorithms for all-pairs approximate shortest paths in weighted graphs (MPI-I-2005-1-003). Saarbrücken: Max-Planck-Institut für Informatik.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-6854-9
Abstract
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.