Recency Queries with Succinct Representation

Authors William L. Holland, Anthony Wirth, Justin Zobel



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Author Details

William L. Holland
  • School of Computing and Information Systems, The University of Melbourne, Parkville, Australia
Anthony Wirth
  • School of Computing and Information Systems, The University of Melbourne, Parkville, Australia
Justin Zobel
  • School of Computing and Information Systems, The University of Melbourne, Parkville, Australia

Acknowledgements

We acknowledge the Wurundjeri People of the Kulin Nations as traditional owners of the land on which we live and work.

Cite As Get BibTex

William L. Holland, Anthony Wirth, and Justin Zobel. Recency Queries with Succinct Representation. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 49:1-49:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.ISAAC.2020.49

Abstract

In the context of the sliding-window set membership problem, and caching policies that require knowledge of item recency, we formalize the problem of Recency on a stream. Informally, the query asks, "when was the last time I saw item x?" Existing structures, such as hash tables, can support a recency query by augmenting item occurrences with timestamps. To support recency queries on a window of W items, this might require Θ(W log W) bits.
We propose a succinct data structure for Recency. By combining sliding-window dictionaries in a hierarchical structure, and careful design of the underlying hash tables, we achieve a data structure that returns a 1+ε approximation to the recency of every item in O(log(ε W)) time, in only (1+o(1))(1+ε)(ℬ+Wlog(ε^(-1))) bits. Here, ℬ is the information-theoretic lower bound on the number of bits for a set of size W, in a universe of cardinality N.

Subject Classification

ACM Subject Classification
  • Theory of computation → Data structures design and analysis
Keywords
  • Succinct Data Structures
  • Data Streams
  • Sliding Dictionary

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