Individual displacements for linear probing hashing with different insertion policies

Abstract

We study the distribution of the individual displacements in hashing with linear probing for three different versions: First Come, Last Come and Robin Hood. Asymptotic distributions and their moments are found when the the size of the hash table tends to infinity with the proportion of occupied cells converging to some α, 0 < α < 1. (In the case of Last Come, the results are more complicated and less complete than in the other cases.)We also show, using the diagonal Poisson transform studied by Poblete, Viola and Munro, that exact expressions for finite m and n can be obtained from the limits as m,n → ∞.We end with some results, conjectures and questions about the shape of the limit distributions. These have some relevance for computer applications.