The analysis of linear probing hashing with buckets: (Extended abstract)

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.