Abstract. We show a two-phase approach for minimizing various communication-cost metrics in fine-grain partitioning of sparse matrices for parallel processing. In the first phase, we obtain a partitioning with the existing tools on the matrix to determine computational loads of the processor. In the second phase, we try to minimize the communicationcost metrics. For this purpose, we develop communication-hypergraph and partitioning models. We experimentally evaluate the contributions on a PC cluster.