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arXiv · 1111.2621

Optimal Lower and Upper Bounds for Representing Sequences

Djamal Belazzougui·Gonzalo Navarro
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Abstract

Sequence representations supporting queries $access$, $select$ and $rank$ are at the core of many data structures. There is a considerable gap between the various upper bounds and the few lower bounds known for such representations, and how they relate to the space used. In this article we prove a strong lower bound for $rank$, which holds for rather permissive assumptions on the space used, and give matching upper bounds that require only a compressed representation of the sequence. Within this compressed space, operations $access$ and $select$ can be solved in constant or almost-constant time, which is optimal for large alphabets. Our new upper bounds dominate all of the previous work in the time/space map.

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Djamal Belazzougui, Gonzalo Navarro. 2011-11-10. Optimal Lower and Upper Bounds for Representing Sequences. https://arxiv.org/abs/1111.2621

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