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Towards an Analysis of Quadratic Probing

Authors William Kuszmaul , Zoe Xi

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Author Details

William Kuszmaul
  • Harvard University, Cambridge, MA, USA
Zoe Xi
  • Massachusetts Institute of Technology, Cambridge, MA, USA

Funding

This work was partially sponsored by the United States Air Force Research Laboratory and the United States Air Force Artificial Intelligence Accelerator and was accomplished under Cooperative Agreement Number FA8750-19-2-1000. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the United States Air Force or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.
  • Kuszmaul, William: Funded by Harvard Rabin Postdoctural Fellowship.
  • Xi, Zoe: Funded by the Carl W. Hoffman and Elizabeth B. Klerman Fund, and by the John Reed Fund.

Cite As Get BibTex

William Kuszmaul and Zoe Xi. Towards an Analysis of Quadratic Probing. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 103:1-103:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ICALP.2024.103

Abstract

Since 1968, one of the simplest open questions in the theory of hash tables has been to prove anything nontrivial about the correctness of quadratic probing. We make the first tangible progress towards this goal, showing that there exists a positive-constant load factor at which quadratic probing is a constant-expected-time hash table. Our analysis applies more generally to any fixed-offset open-addressing hash table, and extends to higher load factors in the case where the hash table examines blocks of some size B = ω(1).

Subject Classification

ACM Subject Classification
  • Theory of computation → Sorting and searching
Keywords
  • quadratic probing
  • hashing
  • open addressing
  • witness trees

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