Optimal Non-Adaptive Cell Probe Dictionaries and Hashing

Authors Kasper Green Larsen , Rasmus Pagh , Giuseppe Persiano , Toniann Pitassi , Kevin Yeo , Or Zamir



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Author Details

Kasper Green Larsen
  • Aarhus University, Denmark
Rasmus Pagh
  • BARC, University of Copenhagen, Denmark
Giuseppe Persiano
  • Università di Salerno, Italy
  • Google, New York, NY, USA
Toniann Pitassi
  • Columbia University, New York, NY, USA
Kevin Yeo
  • Columbia University, New York, NY, USA
  • Google, New York, NY, USA
Or Zamir
  • Tel Aviv University, Israel

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Kasper Green Larsen, Rasmus Pagh, Giuseppe Persiano, Toniann Pitassi, Kevin Yeo, and Or Zamir. Optimal Non-Adaptive Cell Probe Dictionaries and Hashing. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 104:1-104:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ICALP.2024.104

Abstract

We present a simple and provably optimal non-adaptive cell probe data structure for the static dictionary problem. Our data structure supports storing a set of n key-value pairs from [u]× [u] using s words of space and answering key lookup queries in t = O(lg(u/n)/lg(s/n)) non-adaptive probes. This generalizes a solution to the membership problem (i.e., where no values are associated with keys) due to Buhrman et al. We also present matching lower bounds for the non-adaptive static membership problem in the deterministic setting. Our lower bound implies that both our dictionary algorithm and the preceding membership algorithm are optimal, and in particular that there is an inherent complexity gap in these problems between no adaptivity and one round of adaptivity (with which hashing-based algorithms solve these problems in constant time). Using the ideas underlying our data structure, we also obtain the first implementation of a n-wise independent family of hash functions with optimal evaluation time in the cell probe model.

Subject Classification

ACM Subject Classification
  • Theory of computation → Data structures design and analysis
Keywords
  • non-adaptive
  • cell probe
  • dictionary
  • hashing

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