Faster Repetition-Aware Compressed Suffix Trees Based on Block Trees

Abstract

Suffix trees are a fundamental data structure in stringology, but their space usage, though linear, is an important problem for its applications. We design and implement a new compressed suffix tree targeted to highly repetitive texts, such as large genomic collections of the same species. Our suffix tree builds on Block Trees, a recent Lempel-Ziv-bounded data structure that captures the repetitiveness of its input. We use Block Trees to compress the topology of the suffix tree, and augment the Block Tree nodes with data that speeds up suffix tree navigation. Our compressed suffix tree is slightly larger than previous repetition-aware suffix trees based on grammars, but outperforms them in time, often by orders of magnitude. The component that represents the tree topology achieves a speed comparable to that of general-purpose compressed trees, while using 2.3-10 times less space, and might be of interest in other scenarios.

Toward a Definitive Compressibility Measure for Repetitive Sequences

“…We note that it is unknown if a result like Theorem VI.9 can be obtained on a semigroup. For example, it is not known how to compute the minimum of a substring in polylogarithmic time on block trees [43], [35].…”

Smaller RLZ-Compressed Suffix Arrays

“…al. [6], LCSA implementation of Cáceres and Navarro [3], and rlzsa-rand which denotes the best result in [15]. These indexes were selected because r-index is the smallest CSA, rlzsa-rand is the fastest CSA according to experiments [15], and LCSA also uses a differentially encoded SA combined with Re-Pair, instead of RLZ.…”

“…• We compare RLZ-compressed SAs to other state-of-art indexes for repetitive datasets, including those that attempt to exploit repetitions in SA d , such as the LCSA [3,9], showing rlzsa to be significantly faster, and usually smaller.…”