Minimum Cuts in NearLinear Time
Abstract
We significantly improve known time bounds for solving the minimum cut problem on undirected graphs. We use a ``semiduality'' between minimum cuts and maximum spanning tree packings combined with our previously developed random sampling techniques. We give a randomized algorithm that finds a minimum cut in an medge, nvertex graph with high probability in O(m log^3 n) time. We also give a simpler randomized algorithm that finds all minimum cuts with high probability in O(n^2 log n) time. This variant has an optimal RNC parallelization. Both variants improve on the previous best time bound of O(n^2 log^3 n). Other applications of the treepacking approach are new, nearly tight bounds on the number of near minimum cuts a graph may have and a new data structure for representing them in a spaceefficient manner.
 Publication:

arXiv eprints
 Pub Date:
 December 1998
 DOI:
 10.48550/arXiv.cs/9812007
 arXiv:
 arXiv:cs/9812007
 Bibcode:
 1998cs.......12007K
 Keywords:

 Data Structures and Algorithms;
 F.2.2;
 G.2.2;
 G.3