Building Chain and Cactus Representations of All Minimum Cuts from Hao-Orlin in the Same Asymptotic Run Time
A cactus tree is a simple data structure that represents all minimum cuts of a weighted graph in linear space. We describe the first algorithm that can build a cactus tree from the asymptotically fastest deterministic algorithm that finds all minimum cuts in a weighted graph — the Hao-Orlin minimum cut algorithm. This improves the time to construct the cactus in graphs with n vertices and m edges from O(n 3) to O(nmlog n 2/m).
KeywordsSource Node Weighted Graph Source Side Chain Representation Residual Graph
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