Combinatorial Problems in High-Performance Computing: Partitioning

This extended abstract presents a survey of combinatorial problems encountered in scientific computations on today\u27s high-performance architectures, with sophisticated memory hierarchies, multiple levels of cache, and multiple processors on chip as well as off-chip. For parallelism, the most important problem is to partition sparse matrices, graph, or hypergraphs into nearly equal-sized parts while trying to reduce inter-processor communication. Common approaches to such problems involve multilevel methods based on coarsening and uncoarsening (hyper)graphs, matching of similar vertices, searching for good separator sets and good splittings, dynamical adjustment of load imbalance, and two-dimensional matrix splitting methods