Compressed consecutive pattern matching

Abstract

Originating from the work of Navarro and Thankachan [TCS 2016], the problem of consecutive pattern matching is a variant of the fundamental pattern matching problem. In this problem, one is given a text and a pair of patterns $p_1,p_2$, and must compute consecutive occurrences of $p_1,p_2$ in the text. Assuming that the text is given as a straight-line program of size $g$, we develop an algorithm that computes all consecutive occurrences of $p_1,p_2$ in optimal $O(g+\left|p_1\right|+\left|p_2\right|+\mathrm{output})$ time, where $\mathrm{output}$ is the size of the output. As a corollary, we also derive an algorithm that reports all co-occurrences separated by a distance $d\in [a,b]$ in $O(g+\left|p_1\right|+\left|p_2\right|+\mathrm{output})$ time and an algorithm that reports the top-$k$ closest co-occurrences in $O(g+\left|p_1\right|+\left|p_2\right|+k)$ time.