A Coherent Random Number Utilization Scheme for a Fault-tolerant Parallel Execution Model Based on Hierarchical Omission

Abstract

High productivity, scalability, load balancing, and fault tolerance are all important issues of massively parallel computing. A parallel execution model called HOPE, which we are proposing, addresses these issues by “hierarchical omission of redundant computations”. Every HOPE worker performs the entire divide-and-conquer computation with its own planned order, whereas it can omit subcomputations whose results are obtained from other workers at runtime, achieving fault tolerance and parallel efficiency as a team of workers. In most random number generation algorithms, a random number is generated on the basis of the internal state after the previous random number generation. Therefore, simple reordering does not preserve coherent results/conditions among workers based on the properties of utilized random numbers. In order to always use the same sequence for each hierarchical subcomputation, this study explores coherent random number utilization schemes, using Sobol' sequences or the PCG random number generator, which allow generation starting from the latter part by skipping the first part. In addition, the Monte Carlo method is an important application of random numbers. In this study, we examine a HOPE application that computes highly dimensional numerical integrals for pricing securities known as MBS (mortgage-backed securities) using the Monte Carlo method, where the convergence speed of integration errors is independent of dimensionality.