Fast Maximum Matching Algorithm for Bipartite Graphs -

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i trying solve following problem algorithm slow. that's because using edmonds - karp algorithm find maximum flow when applied bipartite graphs gives maximum matching well. it's running time n^5. know faster algorithms solve problem (for bipartite graphs specifically). 1 algorithm studying relabel front n^3.

i write bipartite matching using dinitz's algorithm. there theorem graphs of type of maximum bipartite matching problems has same complexity relabel front(and way easier implement).

in networks arising during solution of bipartite matching problem, number of phases bounded o(\sqrt{v}), therefore leading o(\sqrt{v} e) time bound. resulting algorithm known hopcroft–karp algorithm. more generally, bound holds unit network — network in each vertex, except source , sink, either has single entering edge of capacity one, or single outgoing edge of capacity one, , other capacities arbitrary integers.

unfortunately wikipedia article on algorithm way not enough implement , not find better resource online. have own implementation, have created using guidance others in university long time ago.


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