On partitioning problems with complex objectives

Kamer Kaya, François-Henry Rouet, and Bora Uçar

Abstract. Hypergraph and graph partitioning tools are used to partition work for efficient parallelization of many sparse matrix computations. Most of the time, the objective function that is reduced by these tools relates to reducing communication requirements, and the balancing constraints satisfied by these tools relate to balancing the work or memory requirements. Sometimes, the objective sought for having balance is a complex function of the partition. We describe some important class of parallel sparse matrix computations that have such balance objectives. For these cases, the current state of the art partitioning tools fall short of being adequate. To the best of our knowledge, there is only a single algorithmic framework in the literature to address such balance objectives. We propose another algorithmic framework to tackle complex objectives and experimentally investigate the proposed framework.

Key words. Hypergraph partitioning, Graph partitioning, Sparse matrix partitioning, Parallel sparse matrix computations, Combinatorial scientific computing.