on Karger ’ s Min - Cut Algorithm

Traditionally, the min-cut problem was solved by solving n − 1 min-st-cut problems. In the min-st-cut problem we are given as input two vertices s and t, our aim is to find the set S where s ∈ S and t / ∈ S which minimizes the size of the cut (S, S), i.e., |δ(S)|. The size of the min-st-cut is equal to the value of the max-st-flow (equivalent by linear programming duality). The fastest algorithm for solving max-st-flow runs in O(nm log(n/m)) time [1]. In fact, all n− 1 max-st-flow computations can be done simultaneously with the same time bounds [2].