Abstract of CORC technical report TR-98-01:

Lisa Fleischer, 1998

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 withnvertices andmedges fromO(n³) toO(nmlogn²/m).