Operations, Information and Decisions Papers

Document Type

Journal Article

Date of this Version

11-2011

Publication Source

Combinatorics, Probability and Computing

Volume

20

Issue

6

Start Page

799

Last Page

814

DOI

10.1017/S0963548311000411

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 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.

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Mathematics Commons

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Date Posted: 27 November 2017

This document has been peer reviewed.