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[[Category:Algorithm]] [[Category:Main Algorithm]]

'''Type of algorithm:''' loop ...eventual contents of <math>M</math> will be returned as the result of the algorithm.

'''Also known as:''' ''push-relabel'' algorithm or ''Goldberg-Tarjan'' algorithm '''Type of algorithm:'''

[[Category:Algorithm]] [[Category:Main Algorithm]]

This is a specialization of the [[Preflow-push|generic preflow-push algorithm]]: ...ty|complexity considerations]] for the [[Preflow-push|generic preflow-push algorithm]] yield <math>\mathcal{O}(n^2)</math> relabel operations and forward steps

'''Type of algorithm:''' loop. ...s at termination is called a '''Hungarian forest''' in the literature. The algorithm proves, constructively, that a matching in a bipartite graph is cardinality

'''Type of algorithm:''' loop. # If <math>t</math> is ''not'' seen, the break condition applies, and the algorithm is terminated.

[[Category:Algorithm]] [[Category:Main Algorithm]]

'''Type of algorithm:''' loop. ...of saturating increases of flow values of arcs over all iterations of the main loop is linear in the number of arcs, which is in <math>\mathcal{O}(n^2)</m

'''Type of algorithm:''' loop ...S'</math> of strings, which will eventually hold the overall result of the algorithm.

[[Category:Algorithm]] '''Type of algorithm:''' loop

[[Category: Algorithm]] '''Type of algorithm:''' loop

'''Type of algorithm:''' loop ...ode joins <math>V_i</math>, its key will be irrelevant for the rest of the algorithm.

'''Type of algorithm:''' loop 3 call '''DFS'''(''D''^''T''), but in the main loop of '''DFS''', consider the vertices in order of decreasing ''f''[v] as

'''Type of algorithm:''' loop ...ot \log m)</math> results from sorting all edges in the preprocessing. The main loop has <math>m</math> iteration. There are <math>n-1</math> unite operati

'''Type of algorithm:''' loop. Termination of the main loop will follow from the complexity considerations below. It remains to sh