On greedy construction heuristics for the MAX-CUT problem

Given a graph with non-negative edge weights, the MAXCUT problem is to partition the set of vertices into two subsets so that the sum of the weights of edges with endpoints in different subsets is maximized. This classical NP-hard problem finds applications in VLSI design, statistical physics, and classification among other fields. This paper compares the performance of several greedy construction heuristics for MAX-CUT problem. In particular, a new “worst-out” approach is studied and the proposed edge contraction heuristic is shown to have an approximation ratio of at least 1/3. The results of experimental comparison of the worst-out approach, the well-known best-in algorithm, and modifications for both are also included.