Suffixient Arrays: a New Efficient Suffix Array Compression Technique

Abstract

The Suffix Array is a classic text index enabling on-line pattern matching queries via simple binary search. The main drawback of the Suffix Array is that it takes linear space in the text's length, even if the text itself is extremely compressible. Several works in the literature showed that the Suffix Array can be compressed, but they all rely on complex succinct data structures which in practice tend to exhibit poor cache locality and thus significantly slow down queries. In this paper, we propose a new simple and very efficient solution to this problem by presenting the \emph{Suffixient Array}: a tiny subset of the Suffix Array \emph{sufficient} to locate on-line one pattern occurrence (in general, all its Maximal Exact Matches) via binary search, provided that random access to the text is available. We prove that: (i) the Suffixient Array length $χ$ is a strong repetitiveness measure, (ii) unlike most existing repetition-aware indexes such as the $r$-index, our new index is efficient in the I/O model, and (iii) Suffixient Arrays can be computed in linear time and compressed working space. We show experimentally that, when using well-established compressed random access data structures on repetitive collections, the Suffixient Array $\SuA$ is \emph{simultaneously} (i) faster and orders of magnitude smaller than the Suffix Array $\SA$ and (ii) smaller and \emph{one to two orders of magnitude faster} than the $r$-index. With an average pattern matching query time as low as 3.5 ns per character, our new index gets very close to the ultimate lower bound: the RAM throughput of our workstation (1.18 ns per character).