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Deterministic (2/3 - ε)-Approximation of Matroid Intersection Using Nearly-Linear Independence-Oracle Queries

Author Tatsuya Terao

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ACM Subject Classification
  • Theory of computation → Discrete optimization
  • Mathematics of computing → Matroids and greedoids
  • Theory of computation → Streaming, sublinear and near linear time algorithms
Keywords
  • Matroid intersection
  • approximation algorithm
  • streaming algorithm

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Abstract

In the matroid intersection problem, we are given two matroids ℳ₁ = (V, ℐ₁) and ℳ₂ = (V, ℐ₂) defined on the same ground set V of n elements, and the objective is to find a common independent set S ∈ ℐ₁ ∩ ℐ₂ of largest possible cardinality, denoted by r. In this paper, we consider a deterministic matroid intersection algorithm with only a nearly linear number of independence oracle queries. Our contribution is to present a deterministic O(n/(ε) + r log r)-independence-query (2/3-ε)-approximation algorithm for any ε > 0. Our idea is very simple: we apply a recent Õ(n √r/ε)-independence-query (1 - ε)-approximation algorithm of Blikstad [ICALP 2021], but terminate it before completion. Moreover, we also present a semi-streaming algorithm for (2/3 -ε)-approximation of matroid intersection in O(1/ε) passes.

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Tatsuya Terao. Deterministic (2/3 - ε)-Approximation of Matroid Intersection Using Nearly-Linear Independence-Oracle Queries. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 50:1-50:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.WADS.2025.50

Author Details

Tatsuya Terao
  • Research Institute for Mathematical Sciences, Kyoto University, Japan

Funding

This work was partially supported by the joint project of Kyoto University and Toyota Motor Corporation, titled "Advanced Mathematical Science for Mobility Society" and by JSPS KAKENHI Grant Number JP24KJ1494.

Acknowledgements

The author thanks Yusuke Kobayashi for his generous support and helpful comments on the manuscript.

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