All pairs shortest paths in undirected graphs with integer weights
Shoshan, A.
Zwick, U.
Dept. of Comput. Sci., Tel Aviv Univ.;
This paper appears in: Foundations of Computer Science, 1999. 40th Annual Symposium on
Publication Date: 1999
On page(s): 605-614
Meeting Date: 10/17/1999 - 10/19/1999
Location: New York City, NY, USA
ISBN: 0-7695-0409-4
References Cited: 17
INSPEC Accession Number: 6431150
Digital Object Identifier: 10.1109/SFFCS.1999.814635
Current Version Published: 2002-08-06
Abstract
We show that the all pairs shortest paths (APSP) problem for
undirected graphs with integer edge weights taken from the range {1, 2,
..., M} can be solved using only a logarithmic number of distance
products of matrices with elements in the range (1, 2, ..., M). As a
result, we get an algorithm for the APSP problem in such graphs that
runs in O¯(Mnω) time, where n is the number of
vertices in the input graph, M is the largest edge weight in the graph,
and ω<2.376 is the exponent of matrix multiplication. This
improves, and also simplifies, an
O¯(M(ω+1)/2nω) time algorithm of
Galil and Margalit (1997)
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