Maximum matchings via Gaussian elimination

We present randomized algorithms for finding maximum matchings in general and bipartite graphs. Both algorithms have running time O(n/sup w/), where w is the exponent of the best known matrix multiplication algorithm. Since w < 2.38, these algorithms break through the O(n/sup 2.5/) barrier for th...

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Bibliographic Details
Published in45th Annual IEEE Symposium on Foundations of Computer Science pp. 248 - 255
Main Authors Mucha, M., Sankowski, P.
Format Conference Proceeding
LanguageEnglish
Published Los Alamitos CA IEEE 2004
Subjects
Algorithmics. Computability. Computer arithmetics
Applied sciences
Bipartite graph
Computer science
Computer science; control theory; systems
Exact sciences and technology
Informatics
Matrix decomposition
Partitioning algorithms
Polynomials
Testing
Theoretical computing
Matrix product
Adjacency matrix
Inverse matrix
Randomized algorithm
Adaptation
Random graph
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Summary:We present randomized algorithms for finding maximum matchings in general and bipartite graphs. Both algorithms have running time O(n/sup w/), where w is the exponent of the best known matrix multiplication algorithm. Since w < 2.38, these algorithms break through the O(n/sup 2.5/) barrier for the matching problem. They both have a very simple implementation in time O(n/sup 3/) and the only non-trivial element of the O(n/sup w/) bipartite matching algorithm is the fast matrix multiplication algorithm. Our results resolve a long-standing open question of whether Lovasz's randomized technique of testing graphs for perfect matching in time O(n/sup w/) can be extended to an algorithm that actually constructs a perfect matching.
ISBN:9780769522289
0769522289
ISSN:0272-5428
DOI:10.1109/FOCS.2004.40