Affiliation:
1. Max-Planck-Institut für Informatik
2. University of Michigan
Abstract
The
maximum cardinality
and
maximum weight matching
problems can be solved in
Õ
(
m
√
n
) time, a bound that has resisted improvement despite decades of research. (Here
m
and
n
are the number of edges and vertices.) In this article, we demonstrate that this “
m
√
n
barrier” can be bypassed by approximation. For any
ε
> 0, we give an algorithm that computes a (1 −
ε
)-approximate maximum weight matching in
O
(
mε
−1
log
ε
−1
) time, that is, optimal
linear time
for any fixed
ε
. Our algorithm is dramatically simpler than the best exact maximum weight matching algorithms on general graphs and should be appealing in all applications that can tolerate a negligible relative error.
Funder
Division of Computing and Communication Foundations
United States-Israel Binational Science Foundation
Alexander von Humboldt-Stiftung
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Cited by
123 articles.
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