Random sampling in residual graphs

Abstract

Consider an n-vertex, m-edge, undirected graph with maximum flow value v. We give a new O(m+nv)-time maximum flow algorithm based on finding augmenting paths in random samples of the edges of residual graphs. After assigning certain special sampling probabilities to edges in O(m) time, our algorithm is very simple: repeatedly find an augmenting path in a random sample of edges from the residual graph.