Graph Bisection Algorithins With Good Average Case Behavior

We describe a polynomial time algorithm that, for every input graph, either outputs the minimum bisection of the graph or halts without output. More importantly, we show that the algorithm chooses the former course with high probability for many natural classes of graphs. In particular, for every fixed d⩾3, all suffciently large n and all b = o(n^{1-(1/[(d+1)/2])}, the algorithm finds the minimum bisection for almost all d-regular labelled simple graphs with 2n nodes and bisection width b.