On the graph bisection problem

Some interesting theoretical aspects of graph bisection, a fundamental problem with several applications in the design of very-large-scale-integrated (VLSI) circuits, are presented. Sufficient conditions of optimality are presented, along with a bound on the cost of an optimal bisection. It is then shown that for dense graphs a bisection that approximates an optimal one can be easily found by using a simple greedy method. A class of graphs for which the ratio of an upper and a lower bound on the optimal cost approaches one as the number of vertices in the graph increases is exhibited