Approximate Generalized Matching: $f$-Factors and $f$-Edge Covers

Abstract

In this paper we present linear time approximation schemes for several generalized matching problems on nonbipartite graphs. Our results include $O_{\epsilon }(m)$-time algorithms for $(1-\epsilon )$-maximum weight $f$-factor and $(1+\epsilon )$-approximate minimum weight $f$-edge cover. As a byproduct, we also obtain direct algorithms for the exact cardinality versions of these problems running in $O(m\sqrt{f(V)})$ time. The technical contributions of this work include an efficient method for maintaining {\em relaxed complementary slackness} in generalized matching problems and approximation-preserving reductions between the $f$-factor and $f$-edge cover problems.

References in corpus (1)

• Algebraic Algorithms for b-Matching, Shortest Undirected Paths, and f-Factors

Cited by in corpus (1)

• Fast and Heavy Disjoint Weighted Matchings for Demand-Aware Datacenter Topologies