The Dynamic Longest Increasing Subsequence Problem

In this paper, we construct a data structure using a forest of redblack trees to efficiently compute the longest increasing subsequence of a dynamically updated sequence. Our data structure supports a query for the longest increasing subsequence in O(r + logn) worst case time and supports inserts anywhere in the sequence in O (r logn/r) worst case time, where r is the length of the longest increasing subsequence. The data structure can be augmented to support O(logn) worst case time insertions if the insertions are performed at the end of the sequence. The data structure presented can be augmented to support delete operations in the same time as insertions.