Range Non-Overlapping Indexing

TL;DR

This paper introduces new indexing solutions for efficiently reporting maximal non-overlapping pattern occurrences in a text, including a generalized range version, with optimized space and query time complexities.

Contribution

It presents novel indexing algorithms for non-overlapping and range non-overlapping pattern occurrence queries with improved space and query time bounds.

Findings

O(n) space and O(m + occ_{NO}) query time for non-overlapping indexing

O(n log^ε n) space and O(m + log log n + occ_{ij,NO}) query time for range non-overlapping indexing

Effective solutions for pattern occurrence reporting in large texts

Abstract

We study the non-overlapping indexing problem: Given a text T, preprocess it so that you can answer queries of the form: given a pattern P, report the maximal set of non-overlapping occurrences of P in T. A generalization of this problem is the range non-overlapping indexing where in addition we are given two indexes i,j to report the maximal set of non-overlapping occurrences between these two indexes. We suggest new solutions for these problems. For the non-overlapping problem our solution uses O(n) space with query time of O(m + occ_{NO}). For the range non-overlapping problem we propose a solution with O(n\log^\epsilon n) space for some 0<\epsilon<1 and O(m + \log\log n + occ_{ij,NO}) query time.