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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.
