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

Authors Yasuaki Kobayashi , Kazuhiro Kurita , Kunihiro Wasa

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Author Details

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

Funding

  • Kobayashi, Yasuaki: JSPS KAKENHI Grant Numbers JP20H00595 and JP23H03344
  • Kurita, Kazuhiro: JP21K17812, JP22H03549, JST CREST Grant Number JPMJCR18K3, and JST ACT-X Grant Number JPMJAX2105
  • Wasa, Kunihiro: JSPS KAKENHI Grant Numbers JP22K17849 and JP22H03549, and JST CREST Grant Number JPMJCR18K3

Cite AsGet BibTex

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)
https://doi.org/10.4230/LIPIcs.MFCS.2023.58

Abstract

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
Keywords
  • Polynomial-delay enumeration
  • Ranked Enumeration
  • Matroid intersection
  • Reverse search

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