Fast Approximate Graph Partitioning Algorithms

We study graph partitioning problems on graphs with edge capacities and vertex weights. The problems of b-balanced cuts and k-balanced partitions are unified into a new problem called minimum capacity ρ-separators. A ρ-separator is a subset of edges whose removal partitions the vertex set into connected components such that the sum of the vertex weights in each component is at most ρ times the weight of the graph. We present a new and simple O(log n)approximation algorithm for minimum capacity ρ-separators which is based on spreading metrics yielding an O(log n)-approximation algorithm both for b-balanced cuts and k-balanced partitions. In particular, this result improves the previous best known approximation factor for k-balanced partitions in undirected graphs by a factor of O(log k). We enhance these results by presenting a version of the algorithm that obtains an O(log opt)-approximation factor. The algorithm is based on a technique called spreading metrics that enables us to ...

• Type: Conference
• Year: 1997
• Where: SODA
• Authors: Guy Even, Joseph Naor, Satish Rao, Baruch Schieber
• Keywords: Algorithms, K-balanced Partitions, Minimum Capacity ρ-separator, SODA 1997, Spreading Metrics