## Algebraic Algorithms for Matching and Matroid Problems (2009)

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Venue: | SIAM JOURNAL ON COMPUTING |

Citations: | 11 - 0 self |

### BibTeX

@ARTICLE{Harvey09algebraicalgorithms,

author = {Nicholas J. A. Harvey},

title = {Algebraic Algorithms for Matching and Matroid Problems},

journal = {SIAM JOURNAL ON COMPUTING},

year = {2009},

pages = {2009}

}

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### Abstract

We present new algebraic approaches for two well-known combinatorial problems: non-bipartite matching and matroid intersection. Our work yields new randomized algorithms that exceed or match the efficiency of existing algorithms. For nonbipartite matching, we obtain a simple, purely algebraic algorithm with running time O(n ω) where n is the number of vertices and ω is the matrix multiplication exponent. This resolves the central open problem of Mucha and Sankowski (2004). For matroid intersection, our algorithm has running time O(nr ω−1) for matroids with n elements and rank r that satisfy some natural conditions.