Recency Queries with Succinct Representation

Authors William L. Holland, Anthony Wirth, Justin Zobel

Thumbnail PDF


  • Filesize: 0.53 MB
  • 14 pages

Document Identifiers

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


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

Cite AsGet 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)


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
  • Succinct Data Structures
  • Data Streams
  • Sliding Dictionary


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. Yuriy Arbitman, Moni Naor, and Gil Segev. Backyard cuckoo hashing: Constant worst-case operations with a succinct representation. In FOCS, pages 787-796, 2010. Google Scholar
  2. Eran Assaf, Ran Ben Basat, Gil Einziger, and Roy Friedman. Pay for a sliding Bloom filter and get counting, distinct elements, and entropy for free. In INFOCOM, pages 2204-2212, 2018. Google Scholar
  3. Samy Chambi, Daniel Lemire, Owen Kaser, and Robert Godin. Better bitmap performance with roaring bitmaps. Software: Practice and Experience, 46(5):709-719, 2016. Google Scholar
  4. Martin Dietzfelbinger, Anna Karlin, Kurt Mehlhorn, Friedhelm Meyer Auf Der Heide, Hans Rohnert, and Robert E Tarjan. Dynamic perfect hashing: Upper and lower bounds. SIAM Journal on Computing, 23(4):738-761, 1994. Google Scholar
  5. Zhe Li, Gwendal Simon, and Annie Gravey. Caching policies for in-network caching. In ICCCN, pages 1-7, 2012. Google Scholar
  6. Yang Liu, Wenji Chen, and Yong Guan. Near-optimal approximate membership query over time-decaying windows. In INFOCOM, pages 1447-1455, 2013. Google Scholar
  7. Ahmed Metwally, Divyakant Agrawal, and Amr El Abbadi. Duplicate detection in click streams. In WWW, pages 12-21, 2005. Google Scholar
  8. Moni Naor and Eylon Yogev. Tight bounds for sliding Bloom filters. Algorithmica, 73(4):652-672, 2015. Google Scholar
  9. Rasmus Pagh and Flemming Friche Rodler. Cuckoo hashing. In ESA, pages 121-133, 2001. Google Scholar
  10. Daniel D Sleator and Robert E Tarjan. Amortized efficiency of list update and paging rules. Communications of the ACM, 28(2):202-208, 1985. Google Scholar
  11. Jiansheng Wei, Hong Jiang, Ke Zhou, Dan Feng, and Hua Wang. Detecting duplicates over sliding windows with RAM-efficient detached counting Bloom filter arrays. In NAS, pages 382-391, 2011. Google Scholar