A Serial Multilevel Hypergraph Partitioning Algorithm

Abstract

The graph partitioning problem has many applications in scientific computing such as computer aided design, data mining, image compression and other applications with sparse-matrix vector multiplications as a kernel operation. In many cases it is advantageous to use hypergraphs as they, compared to graphs, have a more general structure and can be used to model more complex relationships between groups of objects. This motivates our focus on the less-studied hypergraph partitioning problem. In this paper, we propose a serial multi-level bipartitioning algorithm. One important step in current heuristics for hypergraph partitioning is clustering during which similar vertices must be recognized. This can be particularly difficult in irregular hypergraphs with high variation of vertex degree and hyperedge size; heuristics that rely on local vertex clustering decisions often give poor partitioning quality. A novel feature of the proposed algorithm is to use the techniques of rough set clustering to address this problem. We show that our proposed algorithm gives on average between 18.8 per cent and 71.1 per cent better quality on these irregular hypergraphs by comparing it to state-of-the-art hypergraph partitioning algorithms on benchmarks taken from real applications.