Weighted selection on coarse-grain hypercubes

Given n weighted records distributed evenly among a p-processor hypercube, p n, we present ee-cient parallel algorithms for solving the weighted selection and related problems in the coarse-grain weak-hypercube model. A special case of the weighted selection problem, in which all the weights are equal, is known as the (unweighted) selection or order statistics problem. Our algorithms seek to minimize separately the time complexity for local computation and that for global communication on coarse-grain hypercubes. Depending on diierent ratios of n=p, we present techniques that lead to eecient hypercube algorithms for separate relative ranges of n and p. Our weighted selection algorithms match the local computation time lower bound of the selection problems on hypercubes for almost all the ratios of n=p. More importantly, the communication time bounds of our algorithms are better even than those of the previously best known hy-percube solutions for the unweighted case in the corresponding relative ranges of n and p. Our algorithms are based on practical hypercube subroutines and make use of a variety of new schemes.