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Succinct Rank Dictionaries Revisited

Authors Saska Dönges , Simon J. Puglisi

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Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • data structures
  • data compression
  • succinct data structures
  • compressed data structures
  • weighted de Bruijn sequence
  • text indexing
  • string algorithms

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Abstract

We study data structures for representing sets of m elements drawn from the universe [0..n-1] that support access and rank queries. A classical approach to this problem, foundational to the fields of succinct and compact data structures, is to represent the set as a bitvector X of n bits, where X[i] = 1 iff i is a member of the set. Our particular focus in this paper is on structures taking log₂{n choose m} + o(n) bits, which stem from the so-called RRR bitvector scheme (Raman et al., ACM Trans. Alg., 2007). In RRR bitvectors, X is conceptually divided into n/b blocks of b bits each. A block containing c 1 bits is then encoded using log₂ b + log₂{b choose c} bits, where log b bits are used to encode c, and log₂{b choose c} bits are used to say which of the {b choose c} possible combinations the block represents. In all existing RRR implementations the code assigned to a block is its lexicographical rank amongst the {b choose c} combinations of its class. In this paper we explore alternative non-lexicographical assignments of codes to blocks. We show these approaches can lead to faster query times and offer relevant space-time trade-offs in practice compared to state-of-the-art implementations (Gog and Petri, Software, Prac. & Exp., 2014) from the Succinct Data Structures Library.

Cite As Get BibTex

Saska Dönges and Simon J. Puglisi. Succinct Rank Dictionaries Revisited. In 23rd International Symposium on Experimental Algorithms (SEA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 338, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.SEA.2025.15

Author Details

Saska Dönges
  • Department of Computer Science, University of Helsinki, Finland
Simon J. Puglisi
  • Department of Computer Science, University of Helsinki, Finland

Acknowledgements

We thank Zsuzsanna Lipták, Taku Onodera, and Rajeev Raman for interesting discussions, and the Finnish Computing Competence Infrastructure (FCCI) for supporting this project with computational and data storage resources.

Supplementary Materials

References

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