Run compressed rank/select for large alphabets

Given a string of length n that is composed of r runs of letters from the alphabet 0,1,..,σ-1 such that 2 ≤ σ ≤ r, we describe a data structure that, provided r ≤ n/log ω(1) n, stores the string in rlog nσ/r + o(r log nσ/r) bits and supports select and access queries in O(log log(n/r)/loglogn) time and rank queries in O(log log(nσ/r)/log time. We show that r log n(σ-1)/r-O(log n/r) bits are necessary for any such data structure and, thus, our solution is succinct. We also describe a data structure that uses (1 + ϵ)r log nσ/r + O(r) bits, where ϵ > 0 is an arbitrary constant, with the same query times but without the restriction r ≤ n/log ω(1) n. By simple reductions to the colored predecessor problem, we show that the query times are optimal in the important case r ≥ 2logδ n, for an arbitrary constant δ > 0. We implement our solution and compare it with the state of the art, showing that the closest competitors consume 31-46% more space. © 2018 IEEE.Peer reviewe