Approximate Generalized Matching: f-Matchings and f-Edge Covers

We present almost linear time approximation schemes for several generalized matching problems on nonbipartite graphs. Our results include O ϵ ( m α ( m , n ) ) -time algorithms for ( 1 - ϵ ) -maximum weight f -matching and ( 1 + ϵ ) -approximate minimum weight f -edge cover. As a byproduct, we also...

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Bibliographic Details
Published inAlgorithmica Vol. 84; no. 7; pp. 1952 - 1992
Main Authors Huang, Dawei, Pettie, Seth
Format Journal Article
LanguageEnglish
Published New York Springer US 01.07.2022
Springer Nature B.V
Subjects
Algorithm Analysis and Problem Complexity
Algorithms
Approximation
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Matching
Mathematical analysis
Mathematics of Computing
Minimum weight
Theory of Computation
Vertex sets
Matching
f-Factors
Edge covers
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Summary:We present almost linear time approximation schemes for several generalized matching problems on nonbipartite graphs. Our results include O ϵ ( m α ( m , n ) ) -time algorithms for ( 1 - ϵ ) -maximum weight f -matching and ( 1 + ϵ ) -approximate minimum weight f -edge cover. As a byproduct, we also obtain direct algorithms for the exact cardinality versions of these problems running in O ( m α ( m , n ) f ( V ) ) time, where f ( V ) is the sum of degree constraint on the entire vertex set. The technical contributions of this work include an efficient method for maintaining relaxed complementary slackness in generalized matching problems and approximation-preserving reductions between the f -matching and f -edge cover problems.
ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-022-00949-5