Optimal-Time Queries on BWT-runs Compressed Indexes

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 $\phi<sup>{-1}$ are two key functions for building indexes on RLBWT, and the best previous result computes LF and $\phi<sup>{-1}$ 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 $\phi<sup>{-1}$ 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.