Explicit and efficient hash families suffice for cuckoo hashing with a stash

Explicit and efficient hash families suffice for cuckoo hashing with a stash

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Bibliographic Details
Statement of responsibility:Martin Aumüller; Martin Dietzfelbinger; Philipp Woelfel
Published in:Algorithmica. - New York, NY : Springer, 1986. - 70(2014), 3, Seite 428-456
Main Author: Aumüller, Martin, 1986- (Author)
Other Authors: Dietzfelbinger, Martin, 1956- (Author) Wölfel, Philipp, 1972- (Author)
Format: electronic Article
Language:English
Published: 2014
ISSN:1432-0541
External Sources:Volltext
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520 |a 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(log n)-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. 
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