Polynomial-Delay Enumeration of Large Maximal Matchings

05/10/2021

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by   Yasuaki Kobayashi, et al.

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Enumerating matchings is a classical problem in the field of enumeration algorithms. There are polynomial-delay enumeration algorithms for several settings, such as enumerating perfect matchings, maximal matchings, and (weighted) matchings in specific orders. In this paper, we present polynomial-delay enumeration algorithms for maximal matchings with cardinality at least given threshold t. Our algorithm enumerates all such matchings in O(nm) delay with exponential space, where n and m are the number of vertices and edges of an input graph, respectively. We also present a polynomial-delay and polynomial-space enumeration algorithm for this problem. As a variant of this algorithm, we give an algorithm that enumerates all maximal matchings in non-decreasing order of its cardinality and runs in O(nm) delay.