Individual displacements for linear probing hashing with different insertion policies

Abstract

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.

Exact distribution of individual displacements in linear probing hashing

“…ACKNOWLEDGMENTS. Several related results, including some of the results presented in this paper, have independently been found by Janson [2005] by related but differently formulated methods. The reader is invited to compare (and combine) the two approaches.…”

“…Then, in Section 5, we derive the exact distribution and limit distributions for the standard algorithm and we conclude with Section 6 where we present the exact and limit distributions for the Robin Hood heuristic. Janson [2005] presents several related results, included some of the results presented in this article. Our methods are different, and we feel that both approaches give complementary light to the understanding of the problem.…”

Parking functions for mappings

“…The functional digraph G f of a 19-mapping f and a sequence s = (10,5,14,10,13,14) of addresses of preferred parking spaces for 6 drivers. All drivers are successful, thus (G f , s) yields a (19,6)-mapping parking function with output-function π (f,s) defined by the sequence (10,5,14,13,12,7) of parking positions of the drivers. root nodes) whose root nodes are connected by directed edges such that they form a cycle.…”

A New Approach to Analyzing Robin Hood Hashing

“…This double-logarithmic behavior also occurs with quite different hashing schemes based on the power of multiple choices [1,11]. Finally, we note that Robin Hood hashing has been also studied extensively in the setting of linear probing schemes [5,14,15].…”