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Compact Data Structures for Collections of Sets

Authors Jarno N. Alanko , Philip Bille , Inge Li Gørtz , Gonzalo Navarro , Simon J. Puglisi

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Subject Classification

ACM Subject Classification
  • Theory of computation → Data structures design and analysis
Keywords
  • Compressed data structures
  • entropy of sets
  • data compression

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Abstract

We define a new entropy measure L(𝒮), called the containment entropy, for a set 𝒮 of sets, which considers the fact that some sets can be contained in others. We show how to represent 𝒮 within space close to L(𝒮) so that any element of any set can be retrieved in logarithmic time. We extend the result to predecessor and successor queries and show how some common set operations can be implemented efficiently.

Cite As Get BibTex

Jarno N. Alanko, Philip Bille, Inge Li Gørtz, Gonzalo Navarro, and Simon J. Puglisi. Compact Data Structures for Collections of Sets. In From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 132, pp. 6:1-6:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/OASIcs.Grossi.6

Author Details

Jarno N. Alanko
  • Department of Computer Science, University of Helsinki, Finland
Philip Bille
  • Technical University of Denmark, Lyngby, Denmark
Inge Li Gørtz
  • Technical University of Denmark, Lyngby, Denmark
Gonzalo Navarro
  • Department of Computer Science, University of Chile, Santiago, Chile
  • Center for Biotechnology and Bioengineering (CeBiB), Santiago, Chile
Simon J. Puglisi
  • Department of Computer Science, University of Helsinki, Finland

Funding

  • Alanko, Jarno N.: Funded by the Helsinki Institute for Information Technology (HIIT).
  • Bille, Philip: Danish Research Council grant DFF-8021-002498.
  • Gørtz, Inge Li: Danish Research Council grant DFF-8021-002498.
  • Navarro, Gonzalo: Basal Funds FB0001 and AFB240001, ANID, Chile.
  • Puglisi, Simon J.: Academy of Finland grant 339070.

Acknowledgements

This work was initiated at the NII Shonan Meeting no. 187 on "Theoretical Foundations of Nonvolatile Memory."

References

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