A new unifying heuristic algorithm for the undirected minimum cut problems using minimum range cut algorithms

Given a connected undirected multigraph with n vertices and m edges, we first propose a new unifying heuristic approach to approximately solving the minimum cut and the s-t minimum cut problems by using efficient algorithms for the corresponding minimum range cut problems. Our method is based on the association of the range value of a cut and its cut value when each edge weight is chosen uniformly randomly from the Bred interval. Our computational experiments demonstrate that this approach produces very good approximate solutions. We shall also propose an O(log(2) n) time parallel algorithm using O(n(2)) processors on an arbitrary CRCW PRAM model for the minimum range cut problems, by which we can efficiently obtain approximate minimum cuts in poly-log time using a polynomial number of processors.