Refined Asymptotics in the Online Selection of an Increasing Subsequence

Abstract

Let vn be the maximum expected length of an increasing subsequence, which can be selected by an online nonanticipating policy from a random sample of size n. Refining known estimates, we obtain an asymptotic expansion of vn up to a O(1) term. The method we use is based on detailed analysis of the dynamic programming equation, and is also applicable to the online selection problem with observations occurring at times of a Poisson process.