A Set of New Mapping and Coloring Heuristics for Distributed-Memory Parallel Processors

Hypergraph-partitioning-based decomposition for parallel sparse-matrix vector multiplication

“…Two basic types of operations are repeatedly performed at each iteration. These are linear operations on dense vectors and sparse-matrix vector product (SpMxV) of the form y Ax, where A is an mÂm square matrix with the same sparsity structure as the coefficient matrix [3], [5], [8], [35], and y and x are dense vectors. Our goal is the parallelization of the computations in the iterative solvers through rowwise or columnwise decomposition of the A matrix as where processor k owns row stripe A r k or column stripe A k , respectively, for a parallel system with u processors.…”

“…In columnwise decomposition, processor k is responsible for computing y k A k x k (where y u kI y k ) and the linear operations on the kth blocks of the vectors. With these decomposition schemes, the linear vector operations can be easily and efficiently parallelized [3], [35] such that only the inner-product computations introduce global communication overhead of which its volume does not scale up with increasing problem size. In parallel SpMxV, the rowwise and columnwise decomposition schemes require communication before or after the local SpMxV computations, thus they can also be considered as pre-and post-communication schemes, respectively.…”

Parallelization of the ILU(0) preconditioner for CFD problems on shared-memory computers

“…For details on the used orderings, see [7]. Also, see [5] for an interesting comparison of scalable orderings. The orderings used in this comparison are the following:…”

“…See [5] for some coloring strategies well adapted to distributed-memory parallel computers. A multi-coloring algorithm applied to the graph of Figure 1 is shown in Figure 3, as well as its associated lower triangular matrix.…”

A comparison of optimization heuristics for the data mapping problem

“…A simple and attractive mapping method considered by many researchers (see [14,22,[37][38][39]) is the so-called data strip or block partitioning heuristic. This heuristic is referred to under different names, some of them are: one-dimensional (1D) strip partitioning, twodimensional (2D) strip partitioning, multilevel load balanced method, median splitting, sector splitting, and block partitioning algorithm.…”