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Applications of a Splitting Trick

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Automata, Languages and Programming (ICALP 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5555))

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Abstract

We study applications of a simple method for circumventing the “full randomness assumption” when building a hashing-based data structure for a set S of keys. The general approach is to “split” S into “pieces” S i , by a splitting hash function. On a piece S i , a method or data structure for generating full randomness is used that uses more space than |S i |. Under certain circumstances, this data structure can be “shared” among the constructions for the pieces S i , which leads to a tighter overall space bound. The method was introduced in the context of cuckoo hashing and its variants, but it seems to have wider applicability. To demonstrate its power and some subtleties, we study three new applications, improving previous constructions: (i) Space-efficient simulation of full randomness on S (following work by Pagh and Pagh (2003/08) and Dietzfelbinger and Woelfel (2003)); (ii) Construction of highly independent functions in the style of Siegel (1989/2004); (iii) One-probe schemes as in work by Buhrman, Miltersen, Radhakrishnan, and Venkatesh (2000/02) and Pagh and Pagh (2002).

Research supported by DFG, Grant Di 412/10-1.

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Authors and Affiliations

  1. Technische Universität Ilmenau, 98693, Ilmenau, Germany

    Martin Dietzfelbinger & Michael Rink

Authors
  1. Martin Dietzfelbinger
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  2. Michael Rink
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Freiburg, Georges Köhler Allee 79, 79110, Freiburg, Germany

    Susanne Albers

  2. Department of Computer and Systems Sciences, Sapienza University of Rome, Via Ariosto 25, 00184, Roma, Italy

    Alberto Marchetti-Spaccamela

  3. Google R&D Center, School of Computer Science, Tel Aviv University, 69978, Tel Aviv, Israel

    Yossi Matias

  4. University of Patras and CTI, N. Kazantzaki Street 1, 26504 Rion, Patras, Greece

    Sotiris Nikoletseas

  5. RWTH Aachen, Lehrstuhl Informatik 7, Ahornstraße 55, 52056, Aachen, Germany

    Wolfgang Thomas

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Dietzfelbinger, M., Rink, M. (2009). Applications of a Splitting Trick. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds) Automata, Languages and Programming. ICALP 2009. Lecture Notes in Computer Science, vol 5555. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02927-1_30

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  • DOI: https://doi.org/10.1007/978-3-642-02927-1_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02926-4

  • Online ISBN: 978-3-642-02927-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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