Counting on General Run-Length Grammars

TL;DR

This paper presents a novel data structure that efficiently counts pattern occurrences in texts compressed with run-length grammars, achieving near-optimal time complexity and solving an open problem in compressed pattern matching.

Contribution

It introduces the first data structure for counting pattern occurrences in run-length grammar compressed texts with space proportional to grammar size and efficient query time.

Findings

Achieves pattern counting in O(m log^{2+ε} n) time.

Uses space proportional to grammar size.

Solves an open problem in compressed pattern matching.

Abstract

We introduce a data structure for counting pattern occurrences in texts compressed with any run-length context-free grammar. Our structure uses space proportional to the grammar size and counts the occurrences of a pattern of length $m$ in a text of length $n$ in time \(O(m\log^{2+\epsilon} n)\), for any constant \(\epsilon > 0\) chosen at indexing time. This is the first solution to an open problem posed by Christiansen et al.~[ACM TALG 2020] and enhances our abilities for computation over compressed data; we give an example application.