2026-07-22T14:20:25Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:24281 2025-11-12T13:39:48Z ddc:004 open_access

Deterministic (2/3 - ε)-Approximation of Matroid Intersection Using Nearly-Linear Independence-Oracle Queries Terao, Tatsuya Matroid intersection approximation algorithm streaming algorithm 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Tatsuya Terao 2025 Is Part Of LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.WADS.2025.50 urn:nbn:de:0030-drops-242812 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.50 eng https://creativecommons.org/licenses/by/4.0/legalcode