Correctness and determinism of Parallel Monte Carlo Processes

Abstract Many natural processes are best modeled by Monte Carlo type algorithms. When parallelizing these, several problems emerge. Some difficulties are well known from parallelizing algorithms in general, such as data coherence or load balancing. Other problems are specific to this kind of algorithm, namely code correctness and deterministic behavior of the code. We illustrate these two problems by describing and iPSC/2 implementation of a simple simulation of population evolution. This paper describes two techniques, the unrolling of an algorithm and the usage of decision dependent random seeds, which may be useful for adapting other dynamic algorithms to parallel computers.

[1]  Ting-Lu Huang,et al.  Parallelism in Connection-Graph-Based Logic Inference , 1988, ICPP.

[2]  Paul O. Frederickson,et al.  A parallel Monte Carlo transport algorithm using a pseudo-random tree to guarantee reproducibility , 1987, Parallel Comput..

[3]  Oliver A. McBryan,et al.  Hypercube Algorithms and Implementations , 1985, PPSC.

[4]  Kenichi Miura,et al.  Tradeoffs in granularity and parallelization for a Monte Carlo shower simulation code , 1988, Parallel Comput..

[5]  M. Peschel,et al.  The Predator-Prey Model: Do We Live in a Volterra World? , 1986 .

[6]  Satoshi Sekiguchi,et al.  Mapping schemes of the particle-in-cell method implemented on the PAX computer , 1988, Parallel Comput..

[7]  Mamoru Maekawa,et al.  Operating Systems: Advanced Concepts , 1987 .

[8]  Ben C. Moszkowski,et al.  Parallel Programming in Temporal Logic , 1987, PARLE.

[9]  Vance Faber,et al.  Modeling the performance of hypercubes: a case study using the particle-in-cell application , 1988, Parallel Comput..

[10]  Reinhard von Hanxleden,et al.  Load Balancing on Message Passing Architectures , 1991, J. Parallel Distributed Comput..

[11]  Trevor Mudge,et al.  Monte Carlo Photon Transport On Shared Memory and Distributed Memory Parallel Processors , 1987 .

[12]  L. R. Scott,et al.  A Comparison of Solutions of Two Model Equations for Long Waves. , 1983 .

[13]  S. M. Ulam,et al.  On Combination of Stochastic and Deterministic Processes , 1947 .

[14]  A. Tanenbaum.  Computer recreations , 1973 .