ON THE ANALYSIS OF LINEAR PROBING HASHING

This paper presents moment analyses and characterizations of limit dis tributions for the construction cost of hash tables under the linear p robing strategy. Two models are considered, that of full tables and th at of sparse tables with a fixed tilling ratio strictly smaller than o ne. For full tables, the construction cost has expectation O(n(3/2)), the standard deviation is of the same order, and a limit law of the Ai ry type holds. (The Airy distribution is a semiclassical distribution that is defined in terms of the usual Airy functions or equivalently i n terms of Bessel functions of indices -1/3, 2/3.) For sparse tables, the construction cost has expectation O(n), standard deviation O(root n), and a limit law of the Gaussian type. Combinatorial relations with other problems leading to Airy phenomena (like graph connectivity, tr ee inversions, tree path length, or area under excursions) are also br iefly discussed.