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The Analysis of Linear Probing Hashing with Buckets

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Abstract.

We present the first exact analysis of a linear probing hashing scheme with buckets of size b . From the generating function for the Robin Hood heuristic we obtain exact expressions for the cost of successful searches. For a full table, with the help of Singularity Analysis, we find the asymptotic expansion of this cost up to O((bm) -1 ) . We conclude with a new approach to study certain recurrences that involve truncated exponentials. A new family of numbers that satisfies a recurrence resembling that of the Bernoulli numbers is introduced. These numbers may prove helpful in studying recurrences involving truncated generating functions.

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Received November 1996; revised March 1997.

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Viola, A., Poblete, P. The Analysis of Linear Probing Hashing with Buckets . Algorithmica 21, 37–71 (1998). https://doi.org/10.1007/PL00009208

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  • DOI: https://doi.org/10.1007/PL00009208

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