Maximum weight bipartite matching in matrix multiplication time

Authors:
Piotr Sankowski
Affiliations:
Institute of Informatics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland
Venue:
Theoretical Computer Science
Year:
2009

Citing 16
Cited 5

Scaling algorithms for network problems

Journal of Computer and System Sciences
Constructing a perfect matching is in random NC

Combinatorica
Matching is as easy as matrix inversion

Combinatorica
Maximum matchings in general graphs through randomization

Journal of Algorithms
Faster scaling algorithms for network problems

SIAM Journal on Computing
Matrix multiplication via arithmetic progressions

Journal of Symbolic Computation - Special issue on computational algebraic complexity
Introduction to algorithms

Introduction to algorithms
Scaling Algorithms for the Shortest Paths Problem

SIAM Journal on Computing
Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems

Journal of the ACM (JACM)
Fast Probabilistic Algorithms for Verification of Polynomial Identities

Journal of the ACM (JACM)
A Decomposition Theorem for Maximum Weight Bipartite Matchings

SIAM Journal on Computing
Probabilistic algorithms for sparse polynomials

EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
High-order lifting and integrality certification

Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Maximum Matchings via Gaussian Elimination

FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Answering distance queries in directed graphs using fast matrix multiplication

FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Shortest paths in matrix multiplication time

ESA'05 Proceedings of the 13th annual European conference on Algorithms

Computing the maximum degree of minors in mixed polynomial matrices via combinatorial relaxation

IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Efficient algorithms for maximum weight matchings in general graphs with small edge weights

Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
A combinatoric interpretation of dual variables for weighted matching and f-factors

Theoretical Computer Science
A simple reduction from maximum weight matching to maximum cardinality matching

Information Processing Letters
Linear-Time Approximation for Maximum Weight Matching

Journal of the ACM (JACM)

Quantified Score

Hi-index	5.23

Visualization

Abstract

In this paper we consider the problem of finding maximum weight matchings in bipartite graphs with nonnegative integer weights. The presented algorithm for this problem works in O@?(Wn^@w) time, where @w is the matrix multiplication exponent, and W is the highest edge weight in the graph. As a consequence of this result we obtain O@?(Wn^@w) time algorithms for computing: minimum weight bipartite vertex cover, single source shortest paths and minimum weight vertex disjoint s-t paths. All of the presented algorithms are randomized and with small probability can return suboptimal solutions.