Refined Asymptotics in the Online Selection of an Increasing Subsequence

Amirlan Seksenbayev

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arXiv · 1808.06300

Refined Asymptotics in the Online Selection of an Increasing Subsequence

Amirlan Seksenbayev

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Abstract

Let $v_n$ 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 $v_n$ 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.

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Amirlan Seksenbayev. 2018-08-20. Refined Asymptotics in the Online Selection of an Increasing Subsequence. https://arxiv.org/abs/1808.06300

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