A Faster Algorithm for Finding Disjoint Paths in Grids
ISAAC '99 Proceedings of the 10th International Symposium on Algorithms and Computation
Solving maximum flow problems on real-world bipartite graphs
Journal of Experimental Algorithmics (JEA)
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
Fast algorithms for weighted bipartite matching
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
A simple reduction from maximum weight matching to maximum cardinality matching
Information Processing Letters
GPU accelerated maximum cardinality matching algorithms for bipartite graphs
Euro-Par'13 Proceedings of the 19th international conference on Parallel Processing
Linear-Time Approximation for Maximum Weight Matching
Journal of the ACM (JACM)
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Periodic global updates of dual variables have been shown to yield a substantial speed advantage in implementations of push-relabel algorithms for the maximum flow and minimum cost flow problems. In this paper, we show that in the context of the bipartite matching and assignment problems, global updates yield a theoretical improvement as well. For bipartite matching, a push-relabel algorithm that uses global updates runs in $O\big(\sqrt n m\frac{\log(n^2/m)}{\log n}\big)$ time (matching the best bound known) and performs worse by a factor of $\sqrt n$ without the updates. A similar result holds for the assignment problem, for which an algorithm that assumes integer costs in the range $[\,-C,\ldots, C\,]$ and that runs in time $O(\sqrt n m\log(nC))$ (matching the best cost-scaling bound known) is presented.