Scientific Communication
Abstract

An Improved Implementation of the Nijenhuis-Wilf Random K-Subset Algorithm
John Burkardt

Nijenhuis and Wilf devised a practical and efficient algorithm for selecting
uniformly at a random a subset of size K from a set of size N.  Their goal
was to produce a sorted result using minimal storage and average labor
O(K).  Their book "Combinatorial Algorithms" [1] includes a detailed explanation,
a generic algorithmic formulation, and a Fortran77 implementation.  However,
the Fortran code does not include comments indicating the corresponding
sections of the algorithm, and moreover, it includes what seems to be a 
programming misstep involving a potential to access uninitialized data.  
In this paper, we explain why the K-subset problem is important, attempt to 
clarify the explanation of the algorithm, and recast the Fortran77 code so
that it is more clear, corresponds to the algorithm, and is more suitable
for easy translation to other languages.  We conclude with some numerical
timings to suggest the performance of the algorithm for a range of values
of K and N, in terms of the uniformity of distribution, and the speed of
execution.

[1] Nijenhuis A., Wilf H., Combinatorial Algorithms for Computers and Calculators,
Second Edition, Academic Press, New York, 1978.