On Stabbing Queries for Generalized Longest Repeat

TL;DR

This paper extends longest repeat queries from point to interval queries, enabling efficient retrieval of all longest repeats covering any interval in a string, with optimal construction and query times, improving usability in applications like computational biology.

Contribution

It introduces a novel indexing structure that supports interval longest repeat queries in optimal time and space, a significant advancement over previous point query methods.

Findings

Supports interval queries in O(1) time after O(n) preprocessing

Finds all longest repeats covering an interval in optimal O(occ) time

Experiments show competitive performance with prior methods

Abstract

A longest repeat query on a string, motivated by its applications in many subfields including computational biology, asks for the longest repetitive substring(s) covering a particular string position (point query). In this paper, we extend the longest repeat query from point query to \emph{interval query}, allowing the search for longest repeat(s) covering any position interval, and thus significantly improve the usability of the solution. Our method for interval query takes a different approach using the insight from a recent work on \emph{shortest unique substrings} [1], as the prior work's approach for point query becomes infeasible in the setting of interval query. Using the critical insight from [1], we propose an indexing structure, which can be constructed in the optimal $O(n)$ time and space for a string of size $n$, such that any future interval query can be answered in $O(1)$ time. Further, our solution can find \emph{all} longest repeats covering any given interval using optimal $O(occ)$ time, where $occ$ is the number of longest repeats covering that given interval, whereas the prior $O(n)$-time and space work can find only one candidate for each point query. Experiments with real-world biological data show that our proposal is competitive with prior works, both time and space wise, while providing with the new functionality of interval queries as opposed to point queries provided by prior works.