Optimal Sequential Selection of a Unimodal Subsequence of a Random Sequence
Probability
2011-10-31 v2 Combinatorics
Optimization and Control
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.
Keywords
Cite
@article{arxiv.1108.2633,
title = {Optimal Sequential Selection of a Unimodal Subsequence of a Random Sequence},
author = {Alessandro Arlotto and J. Michael Steele},
journal= {arXiv preprint arXiv:1108.2633},
year = {2011}
}