Sliding Suffix Tree using LCA

TL;DR

This paper introduces an efficient data structure combining suffix trees, link trees, and LCA to perform real-time substring matching on a sliding window over a character stream, with optimal query and update times.

Contribution

It presents a novel indexed sliding window data structure that supports deterministic substring matching with optimal query and update performance.

Findings

Data structure size is proportional to window size

Query time is proportional to pattern length plus occurrences

Updates are performed in amortized constant time

Abstract

We consider a sliding window $W$ over a stream of characters from some alphabet of constant size. The user wants to perform deterministic substring matching on the current sliding window content and obtain positions of the matches. We present an indexed version of the sliding window using the suffix tree, the link tree and the lowest common ancestor. The data structure of size $\Theta(|W|)$ has optimal time queries $\Theta(m+occ)$ and amortized constant time updates, where $m$ is the length of the query string and $occ$ is the number of its occurrences.