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Simple and Space-Efficient Minimal Perfect Hash Functions

  • Conference paper
Algorithms and Data Structures (WADS 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4619))

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Abstract

A perfect hash function (PHF) h: U →[0,m − 1] for a key set S is a function that maps the keys of S to unique values. The minimum amount of space to represent a PHF for a given set S is known to be approximately 1.44n 2/m bits, where n = |S|. In this paper we present new algorithms for construction and evaluation of PHFs of a given set (for m = n and m = 1.23n), with the following properties:

  1. 1

    Evaluation of a PHF requires constant time.

  2. 1

    The algorithms are simple to describe and implement, and run in linear time.

  3. 1

    The amount of space needed to represent the PHFs is around a factor 2 from the information theoretical minimum.

No previously known algorithm has these properties. To our knowledge, any algorithm in the literature with the third property either:

  • Requires exponential time for construction and evaluation, or

  • Uses near-optimal space only asymptotically, for extremely large n.

Thus, our main contribution is a scheme that gives low space usage for realistic values of n. The main technical ingredient is a new way of basing PHFs on random hypergraphs. Previously, this approach has been used to design simple PHFs with superlinear space usage.

This work was supported in part by GERINDO Project–grant MCT/CNPq/CT-INFO 552.087/02-5, and CNPq Grants 30.5237/02-0 (Nivio Ziviani) and 142786/ 2006-3 (Fabiano C. Botelho).

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Author information

Authors and Affiliations

  1. Dept. of Computer Science, Federal Univ. of Minas Gerais, Belo Horizonte, Brazil

    Fabiano C. Botelho & Nivio Ziviani

  2. Computational Logic and Algorithms Group, IT Univ. of Copenhagen, Denmark

    Rasmus Pagh

Authors
  1. Fabiano C. Botelho
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  2. Rasmus Pagh
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  3. Nivio Ziviani
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Editor information

Frank Dehne Jörg-Rüdiger Sack Norbert Zeh

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Botelho, F.C., Pagh, R., Ziviani, N. (2007). Simple and Space-Efficient Minimal Perfect Hash Functions . In: Dehne, F., Sack, JR., Zeh, N. (eds) Algorithms and Data Structures. WADS 2007. Lecture Notes in Computer Science, vol 4619. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73951-7_13

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  • DOI: https://doi.org/10.1007/978-3-540-73951-7_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73948-7

  • Online ISBN: 978-3-540-73951-7

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