Quickest online selection of an increasing subsequence of specified size1. Issue 2 (15th February 2016)

• Record Type: Journal Article
• Authors: Arlotto, Alessandro; Mossel, Elchanan; Steele, J. Michael
• Is Part Of: Random structures & algorithms. Volume 49:Issue 2(2016)
• Page Start: 235
• Page End: 252
• Publication Date: 2016-02-15
• Subjects: increasing subsequence problem -- online selection -- sequential selection -- time‐focused decision problem -- dynamic programming -- Markov decision problem; Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20634
• Languages: English
• ISSNs: 1042-9832

Abstract

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