2026-07-20T11:27:59Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:21134 2024-09-23T09:13:17Z ddc:004 open_access

Fractional Linear Matroid Matching Is in Quasi-NC Gurjar, Rohit Oki, Taihei Raj, Roshan parallel algorithms hitting set non-commutative rank Brascamp-Lieb polytope algebraic algorithms The matching and linear matroid intersection problems are solvable in quasi-NC, meaning that there exist deterministic algorithms that run in polylogarithmic time and use quasi-polynomially many parallel processors. However, such a parallel algorithm is unknown for linear matroid matching, which generalizes both of these problems. In this work, we propose a quasi-NC algorithm for fractional linear matroid matching, which is a relaxation of linear matroid matching and commonly generalizes fractional matching and linear matroid intersection. Our algorithm builds upon the connection of fractional matroid matching to non-commutative Edmonds' problem recently revealed by Oki and Soma (2023). As a corollary, we also solve black-box non-commutative Edmonds' problem with rank-two skew-symmetric coefficients. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Rohit Gurjar and Taihei Oki and Roshan Raj 2024 Is Part Of LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ESA.2024.63 urn:nbn:de:0030-drops-211344 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.63 eng https://creativecommons.org/licenses/by/4.0/legalcode