A Self-Index on Block Trees

TL;DR

This paper introduces a self-index built on the Block Tree data structure, enabling efficient pattern searches with space close to the original compressed data, based on Lempel-Ziv parsing.

Contribution

It presents a novel self-index on Block Trees that supports pattern search efficiently while maintaining space proportional to the data's compression.

Findings

Uses O(z log(n/z)) space where z is Lempel-Ziv phrases

Finds pattern occurrences in O(m log n + occ log^ε n) time

Supports efficient direct access to compressed text

Abstract

The Block Tree is a recently proposed data structure that reaches compression close to Lempel-Ziv while supporting efficient direct access to text substrings. In this paper we show how a self-index can be built on top of a Block Tree so that it provides efficient pattern searches while using space proportional to that of the original data structure. More precisely, if a Lempel-Ziv parse cuts a text of length $n$ into $z$ non-overlapping phrases, then our index uses $O(z\log(n/z))$ words and finds the $occ$ occurrences of a pattern of length $m$ in time $O(m\log n+occ\log^\epsilon n)$ for any constant $\epsilon>0$.