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Distributional Analysis of the Parking Problem and Robin Hood Linear Probing Hashing with Buckets

Abstract : This paper presents the first distributional analysis of both, a parking problem and a linear probing hashing scheme with buckets of size b. The exact distribution of the cost of successful searches for a b alpha-full table is obtained, and moments and asymptotic results are derived. With the use of the Poisson transform distributional results are also obtained for tables of size m and n elements. A key element in the analysis is the use of a new family of numbers, called Tuba Numbers, that satisfies a recurrence resembling that of the Bernoulli numbers. These numbers may prove helpful in studying recurrences involving truncated generating functions, as well as in other problems related with buckets.
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Alfredo Viola. Distributional Analysis of the Parking Problem and Robin Hood Linear Probing Hashing with Buckets. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2010, Vol. 12 no. 2 (2), pp.307-332. ⟨10.46298/dmtcs.519⟩. ⟨hal-00990469⟩

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