The Minimum Expectation Selection Problem

Details The Minimum Expectation Selection Problem The Minimum Expectation Selection Problem

2001-10-03

arxiv.org/abs/cs/0110011v1

Random Structures and Algorithms 21:278-292, 2002

Computer Science

Data Structures and Algorithms

13 pages, 1 figure. Full version of paper presented at 10th Int. Conf. Random Structures and Algorithms, Poznan, Poland, Augus

Scientific paper

10.1002/rsa.10061

We define the min-min expectation selection problem (resp. max-min 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 min-min expectation problem is NP-complete but admits a fully polynomial time approximation scheme. For d an arbitrary integer, it is NP-hard to approximate the min-min expectation problem with any constant approximation factor. The max-min 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.

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