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The minimum expectation selection problem

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...

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Bibliographic Details
Published in:Random structures & algorithms 2002-10, Vol.21 (3-4), p.278-292
Main Authors: Eppstein, David, Lueker, George S.
Format: Article
Language:English
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Summary: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 within 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. © 2002 Wiley Periodicals, Inc. Random Struct. Alg., 21: 278–292, 2002
ISSN:1042-9832
1098-2418
DOI:10.1002/rsa.10061