We describe methods to support fast rank queries on the Burrows-Wheeler transform (BWT) string$S$of an input string$T$on alphabet$\Sigma$, in order to support pattern counting queries. Our starting point is an approach previously adopted by several authors, which is to represent$S$as$\vert \Sigma\vert$bitvectors, where the bitvector for symbol$c$has a 1 at position$c$if and only if$S[i]=c$, with the bitvec-tors stored in Elias-Fano (EF) encodings, to enable binary rank queries. We first show that the clustering of symbols induced by the BWT makes standard implementations of EF unattractive. We then engineer several improvements to EF that go some way to alleviating this problem, and go on to describe two new EF-inspired bitvectors that have superior practical performance.

Recently it was shown (Puglisi and Zhukova, Proc. SPIRE, 2020) that the suffix array (SA) data structure can be effectively compressed with relative Lempel-Ziv (RLZ) dictionary compression in such a way that arbitrary subar-rays can be rapidly decompressed, thus facilitating compressed indexing. In this paper we describe optimizations to RLZ-compressed SAs, including generation of more effective dictionaries and compact encodings of index components, both of which reduce index size without adversely affecting subarray access speeds relative to other compressed indexes. Our experimental analysis also elucidates the relationship between subarray size and per element access time.