, Volume 70, Issue 3, pp 428–456 | Cite as

Explicit and Efficient Hash Families Suffice for Cuckoo Hashing with a Stash

  • Martin Aumüller
  • Martin Dietzfelbinger
  • Philipp Woelfel


It is shown that for cuckoo hashing with a stash as proposed by Kirsch et al. (Proc. 16th European Symposium on Algorithms (ESA), pp. 611–622, Springer, Berlin, 2008) families of very simple hash functions can be used, maintaining the favorable performance guarantees: with constant stash size s the probability of a rehash is O(1/n s+1), the lookup time and the deletion time are O(s) in the worst case, and the amortized expected insertion time is O(s) as well. Instead of the full randomness needed for the analysis of Kirsch et al. and of Kutzelnigg (Discrete Math. Theor. Comput. Sci., 12(3):81–102, 2010) (resp. Θ(logn)-wise independence for standard cuckoo hashing) the new approach even works with 2-wise independent hash families as building blocks. Both construction and analysis build upon the work of Dietzfelbinger and Woelfel (Proc. 35th ACM Symp. on Theory of Computing (STOC), pp. 629–638, 2003). The analysis, which can also be applied to the fully random case, utilizes a graph counting argument and is much simpler than previous proofs. The results can be generalized to situations where the stash size is non-constant.


Data structures Hash table Randomized algorithms Hash functions Cuckoo hashing Random graphs 



We thank Pascal Klaue for implementing the algorithms and carrying out the experiments presented in Sect. 7. We thank the anonymous reviewers, whose suggestions helped a lot in improving the presentation of this work. We especially thank one reviewer who pointed out the extensions to non-constant stash size and κ-wise independent hash families.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Martin Aumüller
    • 1
  • Martin Dietzfelbinger
    • 1
  • Philipp Woelfel
    • 2
  1. 1.Faculty of Computer Science and AutomationTechnische Universität IlmenauIlmenauGermany
  2. 2.Department of Computer ScienceUniversity of CalgaryCalgaryCanada

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