Fast approximate graph partitioning algorithms

Graph partitioning problems on graphs with edge capacities and vertex weights are considered. The problems of b-balanced and k-multiway separators are unified with the problem of minimum capacity p-separators. A new and simple O(log n) approximation algorithm is developed for minimum capacity p-separators yielding an O(log n) approximation algorithm for both b-balanced cuts and k-multiway separators. The results are enhanced by presenting a version of the algorithm that obtains an O(log OPT) approximation factor. The techniques involve spreading metrics that allow the minimum capacity p-separator problem to be formulated as an integer program. Generalizations of partitioning problems are also treated.