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The highest-label push-relabel algorithm<ref name="cheriyan88"/> organizes all vertices into buckets indexed by their heights. The algorithm always selects an active vertex with the largest height to discharge.
The algorithm has {{nowrap|''O''(''V''<sup>2</sup>{{sqrt|''E''}})}} time complexity. If the lowest-label selection rule is used instead, the time complexity becomes {{nowrap|''O''(''V''<sup>2</sup>''E'')}}.<ref name="ahuja97"/>
===Heuristics===
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