Scaling algorithms for network problems
Journal of Computer and System Sciences
An O(EV log V) algorithm for finding a maximal weighted matching in general graphs
SIAM Journal on Computing
Efficient implementation of graph algorithms using contraction
Journal of the ACM (JACM)
Faster scaling algorithms for network problems
SIAM Journal on Computing
Faster scaling algorithms for general graph matching problems
Journal of the ACM (JACM)
New scaling algorithms for the assignment and minimum mean cycle problems
Mathematical Programming: Series A and B
Clique partitions, graph compression and speeding-up algorithms
Journal of Computer and System Sciences
Data structures for weighted matching and nearest common ancestors with linking
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Deterministic sorting in O(nlog log n) time and linear space
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
A Decomposition Theorem for Maximum Weight Bipartite Matchings
SIAM Journal on Computing
SIAM Journal on Discrete Mathematics
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Maximum skew-symmetric flows and matchings
Mathematical Programming: Series A and B
Maximum Matchings via Gaussian Elimination
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Maximum matching in graphs with an excluded minor
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Equivalence between priority queues and sorting
Journal of the ACM (JACM)
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
A scaling algorithm for weighted matching on general graphs
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Maximum weight bipartite matching in matrix multiplication time
Theoretical Computer Science
Algebraic Algorithms for Matching and Matroid Problems
SIAM Journal on Computing
Multiple-Source Multiple-Sink Maximum Flow in Directed Planar Graphs in Near-Linear Time
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
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 scaling algorithm for maximum weight matching in bipartite graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Linear-Time Approximation for Maximum Weight Matching
Journal of the ACM (JACM)
Hi-index | 0.89 |
Let mcm(m,n) and mwm(m,n,N) be the complexities of computing a maximum cardinality matching and a maximum weight matching, and let mcm"b"i, mwm"b"i be their counterparts for bipartite graphs, where m, n, and N are the edge count, vertex count, and maximum integer edge weight. Kao, Lam, Sung, and Ting (2001) [1] gave a general reduction showing mwm"b"i(m,n,N)=O(N@?mcm"b"i(m,n)) and Huang and Kavitha (2012) [2] recently proved the analogous result for general graphs, that mwm(m,n,N)=O(N@?mcm(m,n)). We show that Gabow@?s mwm"b"i and mwm algorithms from 1983 [3] and 1985 [4] can be modified to replicate the results of Kao et al. and Huang and Kavitha, but with dramatically simpler proofs. We also show that our reduction leads to new bounds on the complexity of mwm on sparse graph classes, e.g., (bipartite) planar graphs, bounded genus graphs, and H-minor-free graphs.