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Random number generation
"... Random numbers are the nuts and bolts of simulation. Typically, all the randomness required by the model is simulated by a random number generator whose output is assumed to be a sequence of independent and identically distributed (IID) U(0, 1) random variables (i.e., continuous random variables dis ..."
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Cited by 139 (30 self)
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Random numbers are the nuts and bolts of simulation. Typically, all the randomness required by the model is simulated by a random number generator whose output is assumed to be a sequence of independent and identically distributed (IID) U(0, 1) random variables (i.e., continuous random variables distributed uniformly over the interval
MAFIA: Efficient and Scalable Subspace Clustering for Very Large Data Sets
, 1999
"... Clustering techniques are used in database mining for finding interesting patterns in high dimensional data. These are useful in various applications of knowledge discovery in databases. Some challenges in clustering for large data sets in terms of scalability, data distribution, understanding en ..."
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Cited by 64 (0 self)
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Clustering techniques are used in database mining for finding interesting patterns in high dimensional data. These are useful in various applications of knowledge discovery in databases. Some challenges in clustering for large data sets in terms of scalability, data distribution, understanding endresults, and sensitivity to input order, have received attention in the recent past. Recent approaches attempt to find clusters embedded in subspaces of high dimensional data. In this paper we propose the use of adaptive grids for efficient and scalable computation of clusters in subspaces for large data sets and large number of dimensions. The bottomup algorithm for subspace clustering computes the dense units in all dimensions and combines these to generate the dense units in higher dimensions. Computation is heavily dependent on the choice of the partitioning parameter chosen to partition each dimension into intervals (bins) to be tested for density. The number of bins determine...
TestU01: A C library for empirical testing of random number generators
 ACM Transactions on Mathematical Software
, 2007
"... 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 ot ..."
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Cited by 32 (1 self)
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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 widelyused software. The tests can be applied to instances of the generators predefined in the library, or to userdefined 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.
Inversive Pseudorandom Number Generators: Concepts, Results And Links
 Proceedings of the 1995 Winter Simulation Conference
, 1995
"... Stochastic simulation requires a reliable source of randomness. Inversive methods are an interesting and very promising new approach to produce uniform pseudorandom numbers. In this paper, we present evidence that these methods are an important contribution to our toolbox. We survey the outstanding ..."
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Cited by 23 (2 self)
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Stochastic simulation requires a reliable source of randomness. Inversive methods are an interesting and very promising new approach to produce uniform pseudorandom numbers. In this paper, we present evidence that these methods are an important contribution to our toolbox. We survey the outstanding performance of inversive pseudorandom number generators in theoretical and empirical tests, in comparison to linear generators. In addition, this paper contains tables of parameters to implement inversive congruential generators. More empirical results as well as an implementation of inversive generators in C are available in the Internet from our Website http:// random.mat.sbg.ac.at. 1 INTRODUCTION Pseudorandom number generators are essential elements in the toolbox of stochastic simulation. Their task is to simulate realizations of independent, identically U([0; 1[)distributed random variables. Other distributions will be obtained by transformation methods, see Devroye (1986), and the...
TestU01: A Software Library in ANSI C for Empirical Testing of Random Number Generators
, 2007
"... 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 spec ..."
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Cited by 19 (2 self)
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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 widelyused 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 userdefined 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.
Combined Generators with Components from Different Families
 Mathematics and Computers in Simulation
, 2003
"... Most random number generators used in practice are based on linear recurrences, with linear output transformations. This gives long periods, fast implementations, and structures that are easy to analyze. But the points produced by these generators have very regular structures. Nonlinear generators c ..."
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Cited by 16 (2 self)
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Most random number generators used in practice are based on linear recurrences, with linear output transformations. This gives long periods, fast implementations, and structures that are easy to analyze. But the points produced by these generators have very regular structures. Nonlinear generators can have less regular structures, but they are generally slower and much harder to analyze when their period is long. In this paper, combined generators with one large linear component, and a second component of a different type (nonlinear or linear), are proposed and studied. The structure of vectors of successive and nonsuccessive output values produced by the combined generators is analyzed. Under mild conditions, these vector sets are proved to have at least as much uniformity than the corresponding sets for the linear component alone. In empirical statistical tests, these combined generators perform better than simple linear generator of comparable period lengths, because of their less regular structure. Efficient implementation methods are suggested.
Random Number Generators: Selection Criteria and Testing
, 1998
"... this paper, we shall assume that the sequence is purely periodic, in the sense that the initial state s 0 is always revisited. In other words, the sequence has no transient part. The goal is to make it hard to distinguish between the output of the generator and a typical realization of an i.i.d. uni ..."
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Cited by 15 (7 self)
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this paper, we shall assume that the sequence is purely periodic, in the sense that the initial state s 0 is always revisited. In other words, the sequence has no transient part. The goal is to make it hard to distinguish between the output of the generator and a typical realization of an i.i.d. uniform sequence over U . In
SPARSE SERIAL TESTS OF UNIFORMITY FOR RANDOM Number Generators
 SIAM JOURNAL ON SCIENTIFIC COMPUTING
, 2002
"... Different versions of the serial test for testing the uniformity and independence of vectors of successive values produced by a (pseudo)random number generator are studied. These tests partition the tdimensional unit hypercube into k cubic cells of equal volume, generate n points (vectors) in this ..."
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Cited by 15 (8 self)
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Different versions of the serial test for testing the uniformity and independence of vectors of successive values produced by a (pseudo)random number generator are studied. These tests partition the tdimensional unit hypercube into k cubic cells of equal volume, generate n points (vectors) in this hypercube, count how many points fall in each cell, and compute a test statistic defined as the sum of values of some univariate function f applied to these k individual counters. Both the overlapping and the nonoverlapping vectors are considered. For different families of generators, such as the linear congruential, Tausworthe, nonlinear inversive, etc., different ways of choosing these functions and of choosing k are compared, and formulas are obtained for the (estimated) sample size required to reject the null hypothesis of i.i.d. uniformity as a function of the period length of the generator. For the classes of alternatives that correspond to linear generators, the most e#cient tests turn out to have k n (in contrast to what is usually done or recommended in simulation books) and use overlapping vectors.
A Collection of Selected Pseudorandom Number Generators with Linear Structures
, 1997
"... 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 app ..."
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Cited by 14 (2 self)
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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. P11143MAT. 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...
A scalable parallel subspace clustering algorithm for massive data sets
 In: Proc. International Conference on Parallel Processing
, 2000
"... Clustering is a data mining problem which finds dense regions in a sparse multidimensional data set. The attribute values and ranges of these regions characterize the clusters. Clustering algorithms need to scale with the data base size and also with the large dimensionality of the data set. Furthe ..."
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Cited by 13 (0 self)
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Clustering is a data mining problem which finds dense regions in a sparse multidimensional data set. The attribute values and ranges of these regions characterize the clusters. Clustering algorithms need to scale with the data base size and also with the large dimensionality of the data set. Further, these algorithms need to explore the embedded clusters in a subspace of a high dimensional space. However, the time complexity of the algorithm to explore clusters in subspaces is exponential in the dimensionality of the data and is thus extremely compute intensive. Thus, parallelization is the choice for discovering clusters for large data sets. In this paper we present a scalable parallel subspace clustering algorithm which has both data and task parallelism embedded in it. We also formulate the technique of adaptive grids and present a truly unsupervised clustering algorithm requiring no user inputs. Our implementation shows near linear speedups with negligible communication overheads. The use of adaptive grids results in two orders of magnitude improvement in the computation time of our serial algorithm over current methods with much better quality of clustering. Performance results on both real and synthetic data sets with very large number of dimensions on a 16 node IBM SP2 demonstrate our algorithm to be a practical and scalable clustering technique. 1.