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@@ -65,9 +65,9 @@ The Hopcroft-Karp algorithm uses the concept of augmenting paths and a level gra
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These steps are repeated until no more augmenting paths can be found, at which point the algorithm terminates with the maximum matching.
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`AIHopcroftCarp>>run` answers the matching cardinality. `AIHopcroftCarp>>matchingEdgeTuples` answers the concrete matching edges (as tuples) after the run.
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`AIHopcroftKarp>>run` answers the matching cardinality. `AIHopcroftKarp>>matchingEdgeTuples` answers the concrete matching edges (as tuples) after the run.
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The Hopcroft-Carp algorithm is basically a special *optimization* of Dinic's algorithm for bipartite unweighted graphs. You find the description of Dinic's algorithm including the augmenting path and level graph concepts in Chapter *@cha:maxflow@*.
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The Hopcroft-Karp algorithm is basically a special *optimization* of Dinic's algorithm for bipartite unweighted graphs. You find the description of Dinic's algorithm including the augmenting path and level graph concepts in Chapter *@cha:maxflow@*.
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### Stable matchings
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From the practical and theoretical points of view, envisaging the special case of bipartite graphs is very common and fructiferous, notably for matching problems.
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Both the greedy and the stable matching algorithm presented here are further examples of using a working list until emptied, like discussed for the topological sorting in this book.
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