Encyclopedia of Algorithms

2016 Edition
| Editors: Ming-Yang Kao

Minimal Perfect Hash Functions

  • Paolo BoldiEmail author
  • Sebastiano Vigna
Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-2864-4_794

Years and Authors of Summarized Original Work

  • 1984; Fredman, Komlós

  • 1984; Mehlhorn

  • 1996; Majewski, Wormald, Havas, Czech

  • 2001; Hagerup, Tholey

  • 2004; Chazelle, Kilian, Rubinfeld, Tal

  • 2007; Botelho, Pagh, Ziviani

  • 2009; Belazzougui, Botelho, Dietzfelbinger

Problem Definition

A minimal perfect hash function (MPHF) is a (data structure providing a) bijective map from a set S of n keys to the set of the first n natural numbers. In the static case (i.e., when the set S is known in advance), there is a wide spectrum of solutions available, offering different trade-offs in terms of construction time, access time, and size of the data structure.

Problem Formulation

Let[x] denote the set of the first x natural numbers. Given a positive integer u=2w,and a set \(S \subseteq [u]\)

Keywords

Minimal perfect hash functions 
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Recommended Reading

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    Belazzougui D, Botelho FC, Dietzfelbinger M (2009) Hash, displace, and compress. In: Fiat A, Sanders P (eds) Algorithms – ESA 2009, 17th annual European symposium, Copenhagen, 7–9 Sept 2009, proceedings, pp 682–693Google Scholar
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    Botelho FC, Pagh R, Ziviani N (2007) Simple and space-efficient minimal perfect hash functions. In: Dehne FKHA, Sack JR, Zeh N (eds) Proceedings of the WADS 2007, 10th international workshop on algorithms and data structures, Halifax. Lecture notes in computer science, vol 4619. Springer, pp 139–150Google Scholar
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    Chazelle B, Kilian J, Rubinfeld R, Tal A (2004) The Bloomier filter: an efficient data structure for static support lookup tables. In: Munro JI (ed) Proceedings of the fifteenth annual ACM-SIAM symposium on discrete algorithms, SODA 2004, New Orleans. SIAM, pp 30–39Google Scholar
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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Dipartimento di InformaticaUniversità degli Studi di MilanoMilanoItaly
  2. 2.Dipartimento di InformaticaUniversità degli Studi di MilanoMilanoItaly