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Combinatorics, Probability and Computing
We consider the problem of selecting sequentially a unimodal subsequence from a sequence of independent identically distributed random variables, and we find that a person doing optimal sequential selection does so within a factor of the square root of two as well as a prophet who knows all of the random observations in advance of any selections. Our analysis applies in fact to selections of subsequences that have d+1 monotone blocks, and, by including the case d= 0, our analysis also covers monotone subsequences.
Arlotto, A., & Steele, J. M. (2011). Optimal Sequential Selection of a Unimodal Subsequence of a Random Sequence. Combinatorics, Probability and Computing, 20 (6), 799-814. http://dx.doi.org/10.1017/S0963548311000411
Date Posted: 27 November 2017
This document has been peer reviewed.