Fast graph partitioning algorithms

The following k-way graph partitioning (GP) problem is considered: given an undirected weighted graph G(V,E), partition the nodes of G into k parts of almost equal size such that the partition-cost (sum of the weights on edges with nodes in different parts) is minimized. Two simple and fast algorithms are proposed, namely, direct algorithm AUCTION and iterative algorithm GREEDYCYCLE. In algorithm AUCTION, the idea of using auction and biddings is introduced using the master-workers paradigm. Algorithm GREEDYCYCLE is a greedy algorithm where the idea of cyclic node passing among parts during the iterative improvement stage is introduced. Cyclic node passing is a k-way generalization of the 2-way node exchange found in the Kernighan-Lin (1970) approach. Experimental results show that, as compared to the existing algorithms, these algorithms are extremely fast, and they produce solutions of reasonable quality.