Scaling algorithms for network problems
Journal of Computer and System Sciences
Constructing a perfect matching is in random NC
Combinatorica
Matrix multiplication via arithmetic progressions
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Maximum matchings in general graphs through randomization
Journal of Algorithms
Faster scaling algorithms for network problems
SIAM Journal on Computing
Introduction to algorithms
Scaling algorithms for the shortest paths problem
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
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)
Matching is as easy as matrix inversion
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Probabilistic algorithms for sparse polynomials
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
ESA '99 Proceedings of the 7th Annual European Symposium on Algorithms
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
An algebraic algorithm for weighted linear matroid intersection
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Fast algorithms for (max, min)-matrix multiplication and bottleneck shortest paths
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Near approximation of maximum weight matching through efficient weight reduction
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
A scaling algorithm for maximum weight matching in bipartite graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Algebraic algorithms for linear matroid parity problems
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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In this paper we consider the problem of finding maximum weighted matchings in bipartite graphs with nonnegative integer weights. The presented algorithm for this problem work in $\tilde{O}(Wn^{\omega})$ time, where ω is the matrix multiplication exponent, and W is the highest edge weight in the graph. As a consequence of this result we obtain $\tilde{O}(Wn^{\omega})$ time algorithms for computing: minimum weight bipartite vertex cover, single source shortest paths and minimum weight vertex disjoint s-t paths.