Optimal-Time Queries on BWT-runs Compressed Indexes

TL;DR

This paper introduces OptBWTR, a new compressed index for highly repetitive strings that supports various queries in optimal time using run-length BWT compression, significantly improving query efficiency.

Contribution

It improves the computation time of LF and ^{-1} functions to constant time and presents the first index supporting multiple queries in optimal time with space proportional to the number of BWT runs.

Findings

LF and ^{-1} are computed in constant time.

OptBWTR supports locate, count, extract queries in optimal time.

The index uses O(r) words of space, where r is the number of BWT runs.

Abstract

Indexing highly repetitive strings (i.e., strings with many repetitions) for fast queries has become a central research topic in string processing, because it has a wide variety of applications in bioinformatics and natural language processing. Although a substantial number of indexes for highly repetitive strings have been proposed thus far, developing compressed indexes that support various queries remains a challenge. The run-length Burrows-Wheeler transform (RLBWT) is a lossless data compression by a reversible permutation of an input string and run-length encoding, and it has received interest for indexing highly repetitive strings. LF and $\phi^{-1}$ are two key functions for building indexes on RLBWT, and the best previous result computes LF and $\phi^{-1}$ in $O(\log \log n)$ time with $O(r)$ words of space for the string length $n$ and the number $r$ of runs in RLBWT. In this paper, we improve LF and $\phi^{-1}$ so that they can be computed in a constant time with $O(r)$ words of space. Subsequently, we present OptBWTR (optimal-time queries on BWT-runs compressed indexes), the first string index that supports various queries including locate, count, extract queries in optimal time and $O(r)$ words of space.