1. Cui Di Supervisor: Andrzej Lingas Lund University
Substantially subcubic approximation schemes for maximum weight bipartite matching
Cui Di
Supervisor: Andrzej Lingas
Lund University
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2. We study the design of relatively fast approximation schemes for maximum weight matching on the base of existing exact algorithms for this problem whose running time is substantially dependent on the maximum edge weight W. The exact algorithms are treated as black box and the general idea of our approach is to eliminate the dependence on W.
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3. Two simple transformations of the edge weights in the input graph G such that a maximum weight matching of the resulting graph yields a close approximation of maximum weight matching of G.
A transformation of a hypothetic exact algorithm for maximum weight matching in a hereditary family of graphs into an approximation scheme.
The running time of the approximation scheme is close to that of the exact algorithm in case the largest edge weight is
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4. Applications
Two approximation schemes for maximum weight matching in a bipartite graph with positive integer edge weights.
· One is more practical and runs in time
· The other one is randomized, uses fast matrix multiplication and runs in time
Extensions
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5. Thank you!
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