A Multilevel Scheme with Adaptive Memory Strategy for Multiway Graph Partitioning

Abstract

The multiway graph partitioning is a problem of finding a partition of the vertex set into a given number of balanced sets whose cut weight is minimum. The multilevel method reduces the size of the graph by shrinking vertices and edges, partitions the smaller graph by using a heuristic, and then expands it to construct a partition for the original graph. We propose an adaptive memory strategy using a multilevel method. It repeats the multilevel method and gradually intensifies the search to promising regions by controlling the way of shrinking the graph in each iteration of the multilevel method. Computational results indicate that this intensification strategy tends to obtain higher quality partitions than repeating the multilevel method independently.