Affiliation:
1. University of Waterloo, Canada
Abstract
We revisit the all-pairs-shortest-paths problem for an unweighted undirected graph with
n
vertices and
m
edges. We present new algorithms with the following running times:
{
O
(
mn
/log
n
) if
m
>
n
log
n
log log log
n
O
(
mn
log log
n
/log
n
) if
m
>
n
log log
n
O
(
n
2
log
2
log
n
/log
n
) if
m
≤
n
log log
n
.
These represent the best time bounds known for the problem for all
m
≪
n
1.376
. We also obtain a similar type of result for the diameter problem for unweighted directed graphs.
Publisher
Association for Computing Machinery (ACM)
Subject
Mathematics (miscellaneous)
Cited by
26 articles.
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