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Tight Thresholds for Cuckoo Hashing via XORSAT

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Automata, Languages and Programming (ICALP 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6198))

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Abstract

We settle the question of tight thresholds for offline cuckoo hashing. The problem can be stated as follows: we have n keys to be hashed into m buckets each capable of holding a single key. Each key has k ≥ 3 (distinct) associated buckets chosen uniformly at random and independently of the choices of other keys. A hash table can be constructed successfully if each key can be placed into one of its buckets. We seek thresholds c k such that, as n goes to infinity, if n/m ≤ c for some c < c k then a hash table can be constructed successfully with high probability, and if n/m ≥ c for some c > c k a hash table cannot be constructed successfully with high probability. Here we are considering the offline version of the problem, where all keys and hash values are given, so the problem is equivalent to previous models of multiple-choice hashing. We find the thresholds for all values of k > 2 by showing that they are in fact the same as the previously known thresholds for the random k-XORSAT problem. We then extend these results to the setting where keys can have differing number of choices, and make a conjecture (based on experimental observations) that extends our result to cuckoo hash tables storing multiple keys in a bucket.

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Author information

Authors and Affiliations

  1. Fakultät für Informatik und Automatisierung, Technische Universität Ilmenau,  

    Martin Dietzfelbinger & Michael Rink

  2. Fakultät für Informatik, Technische Universität Chemnitz,  

    Andreas Goerdt

  3. School of Engineering and Applied Sciences, Harvard University,  

    Michael Mitzenmacher

  4. Electrical Engineering and Statistics Departments, Stanford University,  

    Andrea Montanari

  5. Efficient Computation group, IT University of Copenhagen,  

    Rasmus Pagh

Authors
  1. Martin Dietzfelbinger
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  2. Andreas Goerdt
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  3. Michael Mitzenmacher
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  4. Andrea Montanari
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  5. Rasmus Pagh
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  6. Michael Rink
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Editor information

Editors and Affiliations

  1. Oxford University Computing Laboratory, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK

    Samson Abramsky

  2. Université de Bordeaux (LaBRI) & INRIA, 351, cours de la Libération, 33405, Talence Cedex, France

    Cyril Gavoille

  3. INRIA, Centre de Recherche Bordeaux – Sud-Ouest, 351 cours de la Libération, 33405, Talence Cedex, France

    Claude Kirchner

  4. Heinz Nixdorf Institute, University of Paderborn, Fürstenallee 11, 33102, Paderborn, Germany

    Friedhelm Meyer auf der Heide

  5. University of Patras and RACTI, 26500, Patras, Greece

    Paul G. Spirakis

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Dietzfelbinger, M., Goerdt, A., Mitzenmacher, M., Montanari, A., Pagh, R., Rink, M. (2010). Tight Thresholds for Cuckoo Hashing via XORSAT. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds) Automata, Languages and Programming. ICALP 2010. Lecture Notes in Computer Science, vol 6198. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14165-2_19

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  • DOI: https://doi.org/10.1007/978-3-642-14165-2_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14164-5

  • Online ISBN: 978-3-642-14165-2

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