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arXiv · 1108.2633

Optimal Sequential Selection of a Unimodal Subsequence of a Random Sequence

Alessandro Arlotto·J. Michael Steele
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Abstract

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 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.

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Alessandro Arlotto, J. Michael Steele. 2011-09-24. Optimal Sequential Selection of a Unimodal Subsequence of a Random Sequence. https://doi.org/10.1017/s0963548311000411

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