Polynomial-Delay Enumeration of Large Maximal Common Independent Sets in Two Matroids

Authors Yasuaki Kobayashi , Kazuhiro Kurita , Kunihiro Wasa

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Yasuaki Kobayashi
  • Hokkaido University, Sapporo, Japan
Kazuhiro Kurita
  • Nagoya University, Nagoya, Japan
Kunihiro Wasa
  • Hosei University, Tokyo, Japan

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Yasuaki Kobayashi, Kazuhiro Kurita, and Kunihiro Wasa. Polynomial-Delay Enumeration of Large Maximal Common Independent Sets in Two Matroids. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 58:1-58:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


Finding a maximum cardinality common independent set in two matroids (also known as Matroid Intersection) is a classical combinatorial optimization problem, which generalizes several well-known problems, such as finding a maximum bipartite matching, a maximum colorful forest, and an arborescence in directed graphs. Enumerating all maximal common independent sets in two (or more) matroids is a classical enumeration problem. In this paper, we address an "intersection" of these problems: Given two matroids and a threshold τ, the goal is to enumerate all maximal common independent sets in the matroids with cardinality at least τ. We show that this problem can be solved in polynomial delay and polynomial space. We also discuss how to enumerate all maximal common independent sets of two matroids in non-increasing order of their cardinalities.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Enumeration
  • Polynomial-delay enumeration
  • Ranked Enumeration
  • Matroid intersection
  • Reverse search


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