Before revision:  In this paper , we present a new compressed index on RLBWT, which we call r-index-f, in which r-index is improved for faster locatequeries. in constant time with O(r) words of space, which is a bit step forward in computation time from the previous best result of O(\log \log n) time for string length n and O(r) words of space.
After revision:  In this paper , we present a new compressed index on RLBWT, which we call r-index-f, in which r-index is improved for faster locatequeries., that supports various queries including locate, count, extract queries, decompression and prefix search in the optimal time with smaller working space of O(r) words for small alphabets in this paper. We present efficient data structures for computing two important functions of LF and \phi^{-1 in constant time with O(r) words of space, which is a bit step forward in computation time from the previous best result of O(\log \log n) time for string length n and O(r) words of space.