The Minimum Expectation Selection Problem
Abstract
We define the minmin expectation selection problem (resp. maxmin expectation selection problem) to be that of selecting k out of n given discrete probability distributions, to minimize (resp. maximize) the expectation of the minimum value resulting when independent random variables are drawn from the selected distributions. We assume each distribution has finitely many atoms. Let d be the number of distinct values in the support of the distributions. We show that if d is a constant greater than 2, the minmin expectation problem is NPcomplete but admits a fully polynomial time approximation scheme. For d an arbitrary integer, it is NPhard to approximate the minmin expectation problem with any constant approximation factor. The maxmin expectation problem is polynomially solvable for constant d; we leave open its complexity for variable d. We also show similar results for binary selection problems in which we must choose one distribution from each of n pairs of distributions.
 Publication:

arXiv eprints
 Pub Date:
 October 2001
 DOI:
 10.48550/arXiv.cs/0110011
 arXiv:
 arXiv:cs/0110011
 Bibcode:
 2001cs.......10011E
 Keywords:

 Computer Science  Data Structures and Algorithms;
 Mathematics  Probability;
 F.2.2;
 G.1.6
 EPrint:
 13 pages, 1 figure. Full version of paper presented at 10th Int. Conf. Random Structures and Algorithms, Poznan, Poland, August 2001