An Analysis of the Alias Method for Discrete Random-Variate Generation

Authors:
J. Cole Smith;Sheldon H. Jacobson
Affiliations:
Department of Systems and Industrial Engineering, University of Arizona, P.O. Box 210020, Tucson, Arizona 85721-0020, USA;Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, 1206 West Green Street, Urbana, Illinois 61801, USA
Venue:
INFORMS Journal on Computing
Year:
2005

Citing 2
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Abstract

This paper introduces and studies an optimization problem related to the alias method for discrete random-variate generation. The alias method is an efficient method to generate random variates from a discrete probability distribution. The efficiency of the alias method can be improved by designing the alias table such that the expected number of computations that must be performed per value generated is minimized. The problem of optimizing the construction of the alias table is proven to be strongly NP-hard, even if either of two variations of the alias method relaxing the alias-table-generation restrictions are used. Integer-programming formulations describing these three optimization problems are presented, and insights regarding necessary optimality criteria and relationships among their optimal solutions are discussed.