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arXiv · 1309.7724

The Dynamic Longest Increasing Subsequence Problem

Alex Chen·Timothy Chu·Nathan Pinsker
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Abstract

In this paper, we construct a data structure to efficiently compute the longest increasing subsequence of a sequence subject to dynamic updates. Our data structure supports a query for the longest increasing subsequence in $O(r+\log n)$ worst-case time and supports inserts anywhere in the sequence in $O \left(r\log{n/r}\right)$ worst-case time (where $r$ is the length of the longest increasing subsequence). The same data structure with a minor modification supports $O(\log n)$ worst-case time insertions if the insertions are performed at the end of the sequence. The data structure presented can also be augmented to support delete operations in the same worst-case time as insertions.

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Alex Chen, Timothy Chu, Nathan Pinsker. 2013-09-30. The Dynamic Longest Increasing Subsequence Problem. https://arxiv.org/abs/1309.7724

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