Compressing and Querying Integer Dictionaries Under Linearities and Repetitions

We revisit the fundamental problem of compressing an integer dictionary that supports efficient
${\mathsf {rank}}$
and
${\mathsf {select}}$
operations by exploiting simultaneously two kinds of regularities arising in real data: repetitiveness and approximate linearity. We attack this problem by proposing two novel compressed indexing approaches that extend the classic Lempel-Ziv compression scheme and the more recent block tree data structure with new algorithms and data structures that allow them to also capture regularities in terms of the approximate linearity in the data. Finally, we corroborate these theoretical results with a wide set of experiments on real and synthetic datasets, which allow us to show that our approaches achieve new interesting space-time trade-offs that characterise them as more robust in most practical scenarios compared to the known data structures that exploit only one of the two regularities.