Depth-size trade-offs for parallel prefix computation
Journal of Algorithms
Size-time complexity of Boolean networks for prefix computations
Journal of the ACM (JACM)
Scans as Primitive Parallel Operations
IEEE Transactions on Computers
Journal of the ACM (JACM)
Parallelism in simulation and modeling of scale-free complex networks
Parallel Computing
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Random walks are widely applicable in statistical and scientific computations. Inparticular, they are used in the Monte Carlo method to solve elliptic and parabolic partialdifferential equations (PDEs). This method holds several advantages over other methodsfor PDEs as it solves problems with irregular boundaries and/or discontinuities, givessolutions at individual points, and exhibits great parallelism. However, the generation ofeach random walk in the Monte Carlo method has been done sequentially because eachpoint in the walk is derived from the preceding point by moving one grid step along arandomly selected direction. A parallel algorithm for random walk generation in regular as well as irregular regions is presented. The algorithm is based on parallel prefixcomputations. The communication structure of the algorithm is shown to ideally fit on ahypercube of n nodes, where n is the number of processors.