The bottleneck graph partition problem

The bottleneck graph partition problem is to partition the nodes of a graph into two equally sized sets, so that the maximum edge weight in the cut separating the two sets is minimum. Whereas the graph partition problem, where the sum of the edge weights in the cut is to be minimized, is NP-hard, the bottleneck version is polynomial. This paper describes an O(n²log n) algorithm for the bottleneck graph partition problem, where n is the number of nodes in the graph. We point out two interesting issues related to dynamic algorithms. We also generalize our polynomiality result (for fixed k) to the bottleneck k-cut problem with specified vertices and bounded components.