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Analysis of tree algorithm for collision resolution

Abstract : For the tree algorithm introduced by [Cap79] and [TsMi78] let $L_N$ denote the expected collision resolution time given the collision multiplicity $N$. If $L(z)$ stands for the Poisson transform of $L_N$, then we show that $L_N - L(N) ≃ 1.29·10^-4 \cos (2 π \log _2 N + 0.698)$.
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Laszlo Gyorfi, Sándor Gyori. Analysis of tree algorithm for collision resolution. 2005 International Conference on Analysis of Algorithms, 2005, Barcelona, Spain. pp.357-364, ⟨10.46298/dmtcs.3376⟩. ⟨hal-01184211⟩

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