Algebraic Algorithms for Matching and Matroid Problems
Name
Harvey-2009-ALGEBRAIC ALGORITHMS.pdf
Size
314.23 KB
Format
Adobe PDF
Checksum (MD5)
ec191b0af013031959dbfc61dc3614ff
Author(s)
Harvey, Nicholas J. A.
Date Issued
July 2009
Journal
SIAM Journal on Computing
Publisher
Society for Industrial and Applied Mathematics
Citation
Harvey, Nicholas J. A. “Algebraic Algorithms for Matching and Matroid Problems.” SIAM Journal on Computing 39.2 (2009): 679-702. © 2009 Society for Industrial and Applied Mathematics
Version
Final published version
Abstract
We present new algebraic approaches for two well-known combinatorial problems: nonbipartite 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 $O(n^\omega)$ where $n$ is the number of vertices and $\omega$ is the matrix multiplication exponent. This resolves the central open problem of Mucha and Sankowski (2004). For matroid intersection, our algorithm has running time $O(nr^{\omega-1})$ for matroids with $n$ elements and rank $r$ that satisfy some natural conditions.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
http://dx.doi.org/10.1137/070684008
