The.Algorithm.Design.Manual.Springer-Verlag.1998

Random Number Generation
The Stanford Graphbase (see Section ) contains a machine-independent random number generator
based on the recurrence . With the proper initialization, this generator has a
period of at least .
Algorithm 488 [Bre74], Algorithm 599 [AKD83], and Algorithm 712 [Lev92] of the Collected
Algorithms of the ACM are Fortran codes for generating random numbers according to several
probability distributions, including normal, exponential, and Poisson distributions. They are available
from Netlib (see Section ).
Sim++ is a library of routines for implementing discrete event simulations, built by Robert Cubert and
Paul Fishwick, of the University of Florida. It contains random number generators for a variety of
different distributions, including uniform, exponential, and normal. Check out http://www.cis.ufl.edu/
fishwick/simpack/simpack.html if you need a random number generator to control a simulation.
Fishwick's book [Fis95] describes model design using SimPack.
LEDA (see Section ) provides a comprehensive random source in C++ for generating random bits,
integers, and double precision reals. Sedgewick [Sed92] provides simple implementations of linear and
additive congruential generators in C++. See Section for details.
XTango (see Section ) is an algorithm animation system for UNIX and X-windows, which includes
an animation illustrating the uniformity of random number generation.
Notes: Knuth [Knu81] has a thorough and interesting discussion of random number generation, which I
heartily recommend. He presents the theory behind several methods, including the middle square and
shift-register methods we have not described here, as well as a detailed discussion of statistical tests for
validating random number generators. Another good source is [PFTV86] - our recommended constants
for the linear congruential generator are drawn from here. Comparisons of different random number
generators in practice include [PM88].
Tables of random numbers appear in most mathematical handbooks, as relics from the days before there
was ready access to computers. Most notable is [RC55], which provides one million random digits.
The deep relationship between randomness, information, and compressibility is explored within the
theory of Kolmogorov complexity, which measures the complexity of a string by its compressibility.
Truly random strings are incompressible. The string of seemingly random digits of cannot be random
under this definition, since the entire sequence is defined by any program implementing a series
expansion for . Li and Vitáni [LV93] provide a thorough introduction to the theory of Kolmogorov
complexity.
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