Random number generators are used in many applications, from slot machines to simulations of nuclear reactors. For many computational science applications, such as Monte Carlo simulation, it is crucial that the generators have good randomness properties. This is particularly true for large-scale simulations done on high-performance parallel computers. Good random number generators are hard to find, and many widely-used techniques have been shown to be inadequate. Finding high-quality, efficient algorithms for random number generation on parallel computers is even more difficult. Here we present a review of the most commonly-used random number generators for parallel computers, and evaluate each generator based on theoretical knowledge and empirical tests. In conclusion, we provide recommendations for using random number generators on parallel computers. Outline This review is organized as follows: A brief summary of the findings of this review is first presented, giving an overview of the use of parallel random number generators and a list of recommended algorithms. Section 1 is an introduction to random number generators and their use in computer simulations on parallel computers. Section 2 is a summary of the methods used to test and evaluate random number generators, on both sequential and parallel computers. Section 3 gives an overview of the main algorithms used to implement random number generators on sequential computers, provides examples of software implementations of the algorithms, and states any known problems with the algorithms or implementations. Section 4 gives a description of the most common methods used to parallelize the sequential algorithms, provides examples of software implementing these algorithms, and states any known problems ...

In this paper, we present algorithms that compute the routing and wavelength assignment (RWA) for scheduled lightpath demands in a wavelength-switching mesh network without wavelength conversion functionality. Scheduled lightpath demands are connection demands for which the setup and teardown times are known in advance. We formulate separately the routing problem and the wavelength assignment problem as spatio-temporal combinatorial optimization problems. For the former, we propose a branch and bound algorithm for exact resolution and an alternative tabu search algorithm for approximate resolution. A generalized graph coloring approach is used to solve the wavelength assignment problem. We compared the proposed algorithms to an RWA algorithm that sequentially computes the route and wavelength assignment for the scheduled lightpath demands.

This document describes the software library TestU01, implemented in the ANSI C language, and offering a collection of utilities for the (empirical) statistical testing of uniform random number generators (RNG). The library implements several types of generators in generic form, as well as many specific generators proposed in the literature or found in widely-used software. It provides general implementations of the classical statistical tests for random number generators, as well as several others proposed in the literature, and some original ones. These tests can be applied to the generators predefined in the library and to user-defined generators. Specific tests suites for either sequences of uniform random numbers in [0, 1] or bit sequences are also available. Basic tools for plotting vectors of points produced by generators are provided as well. Additional software permits one to perform systematic studies of the interaction between a specific test and the structure of the point sets produced by a given family of RNGs. That is, for a given kind of test and a given class of RNGs, to determine how large should be the sample size of the test, as a function of the generator’s period length, before the generator starts to fail the test systematically.

We introduce TestU01, a software library implemented in the ANSI C language, and offering a collection of utilities for the empirical statistical testing of uniform random number generators (RNGs). It provides general implementations of the classical statistical tests for RNGs, as well as several others tests proposed in the literature, and some original ones. Predefined tests suites for sequences of uniform random numbers over the interval (0, 1) and for bit sequences are available. Tools are also offered to perform systematic studies of the interaction between a specific test and the structure of the point sets produced by a given family of RNGs. That is, for a given kind of test and a given class of RNGs, to determine how large should be the sample size of the test, as a function of the generator’s period length, before the generator starts to fail the test systematically. Finally, the library provides various types of generators implemented in generic form, as well as many specific generators proposed in the literature or found in widely-used software. The tests can be applied to instances of the generators predefined in the library, or to user-defined generators, or to streams of random numbers produced by any kind of device or stored in files. Besides introducing TestU01, the paper provides a survey and a classification of statistical tests for RNGs. It also applies batteries of tests to a long list of widely used RNGs.

This is a collection of selected linear pseudorandom number that were implemented in commercial software, used in applications, and some of which have extensively been tested. The quality of these generators is examined using scatter plots and the spectral test. In addition, the spectral test is applied to study the applicability of linear congruential generators on parallel architectures. Additional Key Words and Phrases: Pseudorandom number generator, linear congruential generator, multiple recursive generator, combined pseudorandom number generators, parallel pseudorandom number generator, lattice structure, spectral test. 0 0.0001 0 0.0001 0 0.0001 0 0.0001 0 0.0001 Research supported by the Austrian Science Foundation (FWF), project no. P11143-MAT. Contents 1 Linear congruential generator: LCG 5 1.1 LCG(2 31 ; 1103515245; 12345; 12345) ANSIC : : : : : : : : : : : : : : : : 5 1.2 LCG(2 31 \Gamma1; a = 7 5 = 16807; 0; 1) MINSTD : : : : : : : : : : : : : : : : 5 1.3 LCG...

In this paper we investigate the problem of routing a set of lightpath demands for which the set-up and tear-down dates are known. We call this type of requests Foreseeable Lightpath Demands or FLDs. In a transport network, FLDs correspond, for example, to clients' requests for pre-provisioned bandwidth capacity such as fixed-bandwidth pipes for bulk data transfers during the night, extra VPN bandwidth used during peak office working time, etc. Since in some cases the FLDs are not all simultaneous in time, it is possible to reuse physical resources to realize time-disjoint demands. We propose a routing algorithm that takes into account this property to minimize the number of required WDM channels in the physical links of the network. The gain (in terms of saved WDM channels) provided by the algorithm, when compared to a shortest path routing strategy, depends both on the spatial and temporal structure of the set of traffic demands and on the structure of the physical network. The routing problem is formulated as a spatio-temporal combinatorial optimization problem. A Tabu Search meta-heuristic algorithm is developed to solve this problem. I.

: We examine the idea of testing uniform random number generators via two goodness-of-fit statistics: the sum of the logarithms and the sum of squares of overlapping m- spacings. The first statistic is related to an estimator of the entropy of a density and is good to detect clustering, whereas the second one, known as Greenwood's statistic for m = 1, is optimal in terms of Pitman efficiency, in certain setups, among sum-functions of m-spacings. These statistics are asymptotically normally distributed. We evaluate the distance between the standard normal distribution and that of the standardized statistics, as a function of m and of the sample size, when standardization is done using either the asymptotic or the exact (for finite sample size) mean and variance. We then report on experiments with these statistics to detect defects in some popular random number generators. Key Words: Random number generators; statistical tests; spacings. 1 Introduction Let U 1 ; : : : ; U n be a seq...

PRNGlib provides several pseudo-random number generators through a common interface on any Shared or Distributed Memory Parallel architecture. Common routines are specified to initialize the generators with appropriate seeds on each processor and to generate uniform or (normal, Poisson, exponential) distributed random vectors. We concentrate on those generators which assure high quality (i.e., passing most of the empirical and theoretical tests), have a long period, and can be calculated quickly, also in parallel, i.e., it must be possible to generate the same random sequence independent of the number of processors. This splitting facility implies a method to skip over n pseudo-random numbers without calculating all intermediate values, i.e., an O(log n) algorithm is required. Taking into account these criteria Lagged Fibonacci, Generalized Shift Register, and Multiplicative Linear Congruential generators are implemented with (almost) arbitrary specifications for lags, multipliers, m...

Computer models are used in landscape ecology to simulate the effects of human land-use decisions on the environment. Many socioeconomic as well as ecological factors must be considered, requiring the integration of spatially explicit multidisciplinary data. The Land-Use Change Analysis System or LUCAS has been developed to study the effects of land-use on landscape structure in such areas as the Little Tennessee River Basin in western North Carolina and the Olympic Peninsula of Washington state. These effects include land-cover change and species habitat suitability. The map layers used by LUCAS are derived from remotely sensed images, census and ownership maps, topological maps, and output from econometric models. A public-domain geographic information system (GIS) is used to store, display and analyze these map layers. A parallel version of LUCAS (pLUCAS) was developed using the Parallel Virtual Machine (PVM) on a network of workstations giving a speedup factor of 10.77 with 20 node...

Parallel computers are now commonly used for computational science and engineering, and many applications in these areas use random number generators. For some applications, such as large-scale Monte Carlo simulations, it is crucial that the random number generator have good randomness properties. Many programs are available for testing the quality of sequential random number generators, but very little work has been done on testing parallel random number generators. We present some techniques for empirical testing of random number generators on parallel computers, using tests based on computational science applications as examples. In particular, we focus on tests based on parallel algorithms developed for Monte Carlo simulations of the two dimensional Ising model, for which exact results are known. Preliminary results of these tests are presented for several parallel random number generators. Current address. 1 Introduction Parallel computers are now commonly used for computatio...