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Author Duan, Ran ♦ Pettie, Seth
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©2014
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Matching ♦ Approximation ♦ Assignment
Abstract The maximum cardinality and maximum weight matching problems can be solved in $\textit{Õ}(\textit{m}√\textit{n})$ time, a bound that has resisted improvement despite decades of research. (Here $\textit{m}$ and $\textit{n}$ are the number of edges and vertices.) In this article, we demonstrate that this $“\textit{m}√\textit{n}$ barrier” can be bypassed by approximation. For any $\textit{ε}$ > 0, we give an algorithm that computes a (1 ™ $\textit{ε})-approximate$ maximum weight matching in $O(mε^{™1}$ log $ε^{™1})$ time, that is, optimal linear time for any fixed $\textit{ε}.$ 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.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2014-01-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 61
Issue Number 1
Page Count 23
Starting Page 1
Ending Page 23

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Source: ACM Digital Library