Before revision:  Finally, } We introduce a novel division of RLBWT into blocks, which we call balanced BWT-sequence as follows: the RLBWT of a string is divided into several blocks, and a parent-child relationship between each pair of blocks is defined. In addition, we present a novel backward search algorithm on the balanced BWT-sequences, resulting in faster locate queries of r-index-f. We also present new algorithms for solving the queries of count query, extract query, decompression and prefix search on r-index-f .
After revision:  Finally, } We present algorithms for computing queries on RLBWT by leveraging those two data structures in optimal time with O(r) words of space .