Sequential Selection of a Monotone Subsequence from a Random Permutation
Probability
2015-09-16 v1
Abstract
We find a two term asymptotic expansion for the optimal expected value of a sequentially selected monotone subsequence from a random permutation of length n. A striking feature of this expansion is that tells us that the expected value of optimal selection from a random permutation is quantifiably larger than optimal sequential selection from an independent sequences of uniformly distributed random variables; specifically, it is larger by at least (1/6)log n +O(1).
Cite
@article{arxiv.1509.04617,
title = {Sequential Selection of a Monotone Subsequence from a Random Permutation},
author = {Peichao Peng and J. Michael Steele},
journal= {arXiv preprint arXiv:1509.04617},
year = {2015}
}