Building Chain and Cactus Representations of All Minimum Cuts from Hao-Orlin in the Same Asymptotic Run Time

  • Lisa Fleischer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1412)


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).


Source Node Weighted Graph Source Side Chain Representation Residual Graph 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Lisa Fleischer
    • 1
  1. 1.Department of Industrial Engineering and Operations ResearchColumbia UniversityNew YorkUSA

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