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FOCS
2006
IEEE

Algebraic Structures and Algorithms for Matching and Matroid Problems

8 years 9 months ago
Algebraic Structures and Algorithms for Matching and Matroid Problems
We present new algebraic approaches for several wellknown combinatorial problems, including non-bipartite matching, matroid intersection, and some of their generalizations. Our work yields new randomized algorithms that are the most efficient known. For non-bipartite matching, we obtain a simple, purely algebraic algorithm with running time O(nω ) 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(nrω−1 ) for matroids with n elements and rank r that satisfy some natural conditions. This algorithm is based on new algebraic results characterizing the size of a maximum intersection in contracted matroids. Furthermore, the running time of this algorithm is essentially optimal.
Nicholas J. A. Harvey
Added 11 Jun 2010
Updated 11 Jun 2010
Type Conference
Year 2006
Where FOCS
Authors Nicholas J. A. Harvey
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