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 ?^{-1} are two key functions for building indexes on RLBWT, and the best previous result computes LF and ?^{-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 ?^{-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
