Between min cut and graph bisection

Abstract

We investigate a class of graph partitioning problems whose two extreme representatives are the well-known Min Cut and Graph Bisection problems. The former is known to be efficiently solvable by flow techniques, the latter to be NP-complete. The results presented in this paper are - a monotony result of the type “The more balanced the partition we look for has to be, the harder the problem”. - a complexity result, clarifying the status of a large part of intermediate problems in the class. Thus we show the existence and partly localize an “efficiency border” between the two extremes.