Abstract not found

This paper presents moment analyses and characterizations of limit distributions for the construction cost of hash tables under the linear probing strategy. Two models are considered, that of full tables and that of sparse tables with a fixed filling ratio strictly smaller than one. For full tables, the construction cost has expectation O(n3/2), the standard deviation is of the same order, and a limit law of the Airy type holds. (The Airy distribution is a semiclassical distribution that is defined in terms of the usual Airy functions or equivalently in terms of Bessel functions of indices − 1 2 3, 3.) For sparse tables, the construction cost has expectation O(n), standard deviation O ( √ n), and a limit law of the Gaussian type. Combinatorial relations with other problems leading to Airy phenomena (like graph connectivity, tree inversions, tree path length, or area under excursions) are also briefly discussed.

This paper provides tight bounds for the moments of the width of rooted labeled trees with n nodes, answering an open question of Odlyzko and Wilf (1987). To this aim, we use one of the many one-to-one correspondences between trees and parking functions, and also a precise coupling between parking functions and the empirical processes of mathematical statistics. Our result turns out to be a consequence of the strong convergence of empirical processes to the Brownian bridge (Komlos, Major and Tusnady, 1975).

This paper analyzes various algorithms for scheduling low priority disk drive tasks. The derived closed form solution is applicable to class of greedy algorithms that include a variety of background disk scanning applications. By paying close attention to many characteristics of modern disk drives, the analytical solutions achieve very high accuracy---the difference between the predicted response times and the measurements on two different disks is only 3% for all but one examined workload. This paper also proves a theorem which shows that background tasks implemented by greedy algorithms can be accomplished with very little seek penalty. Using greedy algorithm gives a 10% shorter response time for the foreground application requests and up to a 20% decrease in total background task run time compared to results from previously published techniques.

Abstract. Starting with a monodisperse configuration with n size–1 particles, an additive Marcus–Lushnikov process evolves until it reaches its final state (a unique particle with mass n). At each of the n − 1 steps of its evolution, a merging cost is incurred, that depends on the sizes of the two particles involved, and on an independent random factor. This paper studies the asymptotic behaviour of the cumulated costs up to the kth clustering, under various regimes for (n, k), with applications to the study of Union–Find algorithms.