Quickest online selection of an increasing subsequence of specified size |
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| Authors: | Alessandro Arlotto Elchanan Mossel J Michael Steele |
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| Institution: | 1. The Fuqua School of Business, Duke University, Durham, North Carolina;2. Wharton School, Department of Statistics, Huntsman Hall 459, University of Pennsylvania, Philadelphia, Pennsylvania 19104 and Department of Statistics, University of California, Berkeley, California;3. Wharton School, Department of Statistics, Huntsman Hall 447, University of Pennsylvania, Philadelphia, Pennsylvania |
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| Abstract: | Given a sequence of independent random variables with a common continuous distribution, we consider the online decision problem where one seeks to minimize the expected value of the time that is needed to complete the selection of a monotone increasing subsequence of a prespecified length n. This problem is dual to some online decision problems that have been considered earlier, and this dual problem has some notable advantages. In particular, the recursions and equations of optimality lead with relative ease to asymptotic formulas for mean and variance of the minimal selection time. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 235–252, 2016 |
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| Keywords: | increasing subsequence problem online selection sequential selection time‐focused decision problem dynamic programming Markov decision problem |
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