One-dimensional partitioning for heterogeneous systems: Theory and practice
Journal of Parallel and Distributed Computing
Load-balancing spatially located computations using rectangular partitions
Journal of Parallel and Distributed Computing
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Optimal load balancing in sparse matrix decompositionwithout disturbing the row/column ordering is investigated.Both asymptotically and run-time efficient exact algorithmsare proposed and implemented for one-dimensional (1D)striping and two-dimensional (2D) jagged partitioning. Binarysearch method is successfully adopted to 1D striped decompositionby deriving and exploiting a good upper boundon the value of an optimal solution. A binary search algorithmis proposed for 2D jagged partitioning by introducinga new 2D probing scheme. A new iterative-refinementscheme is proposed for both 1D and 2D partitioning. Proposedalgorithms are also space efficient since they onlyneed the conventional compressed storage scheme for thegiven matrix, avoiding the need for a dense workload matrixin 2D decomposition. Experimental results on a wideset of test matrices show that considerably better decompositionscan be obtained by using optimal load balancingalgorithms instead of heuristics. Proposed algorithms are100 times faster than a single sparse-matrix vector multiplication(SpMxV), in the 64-way 1D decompositions, on theoverall average. Our jagged partitioning algorithms areonly 60% slower than a single SpMxV computation in the8\times8-way 2D decompositions, on the overall average.