Random Number Generation on Parallel Computers

2001 Fiscal Year Final Research Report Summary

• Project/Area Number: 11680327
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Statistical science
• Research Institution: Tokyo University of Science
• Principal Investigator: NIKI Naoto Science University of Tokyo, Dept. Manag. Sci., Professor, 工学部, 教授 (10000209)
• Co-Investigator(Kenkyū-buntansha): HASHIGUCHI Hiroki Science Univ. Tokyo, Dept. Manag. Sci., Res. Associate, 工学部, 助手 (50266920)
• Project Period (FY): 1999 – 2000
• Keywords: Random Number / Parallel Computing / Independent Sequence / Reproductivity / Monte Carlo Computation / PVM / KLIC / Finite Field Arithmetic

Research Abstract

The algebraic random number generator due to Niki, based on finite field arithmetics on GF(p^n) for a large prime p(2^<24>-3, for example) and an integer η around 12 or larger, is extended for use in parallel Monte Carlo computations, by dividing a period of length p^n-1 into many subsequences and each of which is associated with a parallel process
Our main concerns in parallelization are (1)independence between extremely long sequences of random numbers ; (2)reproductivity of results from parallel Monte Carlo computations, in other words, providing the same seed corresponding to each of parallel processes which may be asynchronously initiated in varied order of time ; and (3)seeding to dynamically originated processes and recycling the remaining parts of sequences untouched by processes already killed.
Independence (1)as well as equi-distribution is approved both by mathematical evaluation of errors and by a series of statistical tests on the results from a number of experiments in generation of parallel random numbers.
We have proposed a procedure for reproduction (2)of the same results, in spite of undetermined property in time order of parallel computation, when the number of active processes is fixed and not so huge. It is remained for future work, however, to reduce the overheads for realization of reproductivity.
If we limit our computations to those on a master-slave architecture system, there seems to be several methods for heavily dynamic problems (3)worth to try. But, for more promising pier-to pier type architecture, it is difficult to find a truly effective solution.