The Minimum Bisection in the Planted Bisection Model

In the planted bisection model a random graph G(n, p+, p−) with n vertices is created by partitioning the vertices randomly into two classes of equal size (up to ±1). Any two vertices that belong to the same class are linked by an edge with probability p+ and any two that belong to different classes with probability p− < p+ independently. The planted bisection model has been used extensively to benchmark graph partitioning algorithms. If p± = 2d±/n for numbers 0 ≤ d− < d+ that remain fixed as n→∞, then w.h.p. the “planted” bisection (the one used to construct the graph) will not be a minimum bisection. In this paper we derive an asymptotic formula for the minimum bisection width under the assumption that d+ − d− > c √ d+ ln d+ for a certain constant c > 0. 1998 ACM Subject Classification G.2.2 Graph Theory