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Quasi Monte Carlo Integration in Grid Environments: Further Leaping Effects

The splitting of Quasi-Monte Carlo (QMC) point sequences into interleaved substreams has been suggested to raise the speed of distributed numerical integration and to lower the traffic on the network. The usefulness of this approach in GRID environments is discussed. After specifying requirements for using QMC techniques in GRID environments in general we review and evaluate the proposals made in literature so far. In numerical integration experiments we investigate the quality of single leaped QMC point sequence substreams, comparing the respective properties of Sobol', Halton, Faure, Niederreiter-Xing, and Zinterhof sequences in detail. Numerical integration results obtained on a distributed system show that leaping sensitivity varies tremendously among the different sequences and we provide examples of deteriorated results caused by leaping effects, especially in heterogeneous settings which would be expected in GRID environments.