Almost-optimum speed-ups of algorithms for bipartite matching and related problems
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
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
Faster scaling algorithms for general graph matching problems
Journal of the ACM (JACM)
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
High-speed switch scheduling for local-area networks
ACM Transactions on Computer Systems (TOCS)
Scaling Algorithms for the Shortest Paths Problem
SIAM Journal on Computing
Clique partitions, graph compression and speeding-up algorithms
Journal of Computer and System Sciences
The iSLIP scheduling algorithm for input-queued switches
IEEE/ACM Transactions on Networking (TON)
Data structures for weighted matching and nearest common ancestors with linking
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
An Efficient Implementation of Edmonds' Algorithm for Maximum Matching on Graphs
Journal of the ACM (JACM)
A Decomposition Theorem for Maximum Weight Bipartite Matchings
SIAM Journal on Computing
SIAM Journal on Discrete Mathematics
A New Approach to Maximum Matching in General Graphs
ICALP '90 Proceedings of the 17th International Colloquium on Automata, Languages and Programming
ESA '95 Proceedings of the Third Annual European Symposium on Algorithms
Maximum Matchings via Gaussian Elimination
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Algebraic Structures and Algorithms for Matching and Matroid Problems
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
An O(v|v| c |E|) algoithm for finding maximum matching in general graphs
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
Scaling algorithms for network problems
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
A n5/2 algorithm for maximum matchings in bipartite
SWAT '71 Proceedings of the 12th Annual Symposium on Switching and Automata Theory (swat 1971)
Maximum weight bipartite matching in matrix multiplication time
Theoretical Computer Science
Perfect matchings in o(n log n) time in regular bipartite graphs
Proceedings of the forty-second ACM symposium on Theory of computing
Approximating Maximum Weight Matching in Near-Linear Time
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
A scaling algorithm for maximum weight matching in bipartite graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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)
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Let G = (V, E) be a graph with positive integral edge weights. Our problem is to find a matching of maximum weight in G. We present a simple iterative algorithm for this problem that uses a maximum cardinality matching algorithm as a subroutine. Using the current fastest maximum cardinality matching algorithms, we solve the maximum weight matching problem in O(W √nm logn(n2/m)) time, or in O(Wnω) time with high probability, where n = |V|, m = |E|, W is the largest edge weight, and ω W = o(log1.5 n). Our technique hinges on exploiting Edmonds' matching polytope and its dual.