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Conference Papers Discrete Mathematics and Theoretical Computer Science Year : 2006

Bipartite Random Graphs and Cuckoo Hashing

Abstract

The aim of this paper is to extend the analysis of Cuckoo Hashing of Devroye and Morin in 2003. In particular we make several asymptotic results much more precise. We show, that the probability that the construction of a hash table succeeds, is asymptotically $1-c(\varepsilon)/m+O(1/m^2)$ for some explicit $c(\varepsilon)$, where $m$ denotes the size of each of the two tables, $n=m(1- \varepsilon)$ is the number of keys and $\varepsilon \in (0,1)$. The analysis rests on a generating function approach to the so called Cuckoo Graph, a random bipartite graph. We apply a double saddle point method to obtain asymptotic results covering tree sizes, the number of cycles and the probability that no complex component occurs.
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Dates and versions

hal-01184689 , version 1 (17-08-2015)

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Reinhard Kutzelnigg. Bipartite Random Graphs and Cuckoo Hashing. Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, 2006, Nancy, France. pp.403-406, ⟨10.46298/dmtcs.3486⟩. ⟨hal-01184689⟩

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