Analysis A Fast Matching Algorithm

Analysis We will show that after at mostn reweighting steps the size of the maximum matching can be increased by finding an augmenting path. This gives a polynomial running time. EADS 21 Weighted Bipartite Matching c Ernst Mayr, Harald Räcke 565 Analysis How do we findS? Start on the left and compute an alternating tree, starting at any free nodeu. If this construction stops, there is no perfect matching in the tight subgraph (because for a

perfect matching we need to find an augmenting path starting at u). The set of even vertices is on the left and the set of odd vertices is on the right and contains all neighbours of even nodes. All odd vertices are matched to even vertices. Furthermore, the even vertices additionally contain the free vertexu. Hence,jVoddj j Veven j
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