Fractional Linear Matroid Matching is in quasi-NC
CoRR(2024)
摘要
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.
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