Hsien-Kuei Hwang

Learn More
We propose a uniform approach to describing the phase change of the limiting distribution of space measures in random m-ary search trees: the space requirement, when properly normalized, is asymptotically normally distributed for m ≤ 26 and does not have a fixed limit distribution for m > 26. The tools are based on the method of moments and asymptotic(More)
Flajolet and Soria established several central limit theorems for the parameter “number of components” in a wide class of combinatorial structures. In this paper, we shall prove a simple theorem which applies to characterize the convergence rates in their central limit theorems. This theorem is also applicable to arithmetical functions. Moreover, asymptotic(More)
Cauchy–Euler differential equations surfaced naturally in a number of sorting and searching problems, notably in quicksort and binary search trees and their variations. Asymptotics of coefficients of functions satisfying such equations has been studied for several special cases in the literature. We study in this paper a very general framework for(More)
We characterize all limit laws of the quicksort type random variables defined recursively by Xn d = XIn + X ∗ n−1−In + Tn when the “toll function” Tn varies and satisfies general conditions, where (Xn), (X ∗ n ), (In, Tn) are independent, Xn d = X∗ n , and In is uniformly distributed over {0, . . . , n − 1}. When the “toll function” Tn (cost needed to(More)
A fine analysis is given of the transitional behavior of the average cost of quicksort with median-of-three. Asymptotic formulae are derived for the stepwise improvement of the average cost of quicksort when iterating median-of-threek rounds for all possible values ofk. The methods used are general enough to apply to quicksort with median-of-(2t + 1) and to(More)
Poisson approximation has received extensive interest in recent probability literature. The general problem is to derive bounds on the closeness of a suitable Poisson distribution to the distribution in question (usually of discrete type). To measure the degree of proximity of Poisson approximation, the following distances are usually introduced: for any(More)
Let X = {x1,x2, . . . ,xn} be a set of independent and identically distributed (iid) random vectors in Rd. A point xi = (xi1, . . . , xid) is said to be dominated by xj if xik < xjk for all k = 1, . . . , d; and a point xi is called a maximum of X if none of the other points dominates it. This paper is concerned with the number of maxima, denoted by Kn,d,(More)
We summarize several limit results for the profile of random plane-oriented recursive trees. These include the limit distribution of the normalized profile, asymptotic bimodality of the variance, asymptotic approximations of the expected width and the correlation coefficients of two level sizes. We also unveil an unexpected connection between the profile of(More)