License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2020.49
URN: urn:nbn:de:0030-drops-133931
URL: https://drops.dagstuhl.de/opus/volltexte/2020/13393/
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Holland, William L. ; Wirth, Anthony ; Zobel, Justin

Recency Queries with Succinct Representation

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LIPIcs-ISAAC-2020-49.pdf (0.5 MB)

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.

BibTeX - Entry

@InProceedings{holland_et_al:LIPIcs:2020:13393,
  author =	{William L. Holland and Anthony Wirth and Justin Zobel},
  title =	{{Recency Queries with Succinct Representation}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{49:1--49:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Yixin Cao and Siu-Wing Cheng and Minming Li},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/13393},
  URN =		{urn:nbn:de:0030-drops-133931},
  doi =		{10.4230/LIPIcs.ISAAC.2020.49},
  annote =	{Keywords: Succinct Data Structures, Data Streams, Sliding Dictionary}
}

Keywords: Succinct Data Structures, Data Streams, Sliding Dictionary
Collection: 31st International Symposium on Algorithms and Computation (ISAAC 2020)
Issue Date: 2020
Date of publication: 04.12.2020

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