Browsing by Author "Lee, Chung-Kuei"

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A General Central Limit Theorem for Shape Parameters of m-ary Tries and PATRICIA Tries
(2014-03-24)
Fuchs, Michael
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Lee, Chung-Kuei
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應用數學系
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Department of Applied Mathematics
Tries and PATRICIA tries are fundamental data structures in computer science with numerous applications. In a recent paper, a general framework for obtaining the mean and variance of additive shape parameters of tries and PATRICIA tries under the Bernoulli model was proposed. In this note, we show that a slight modification of this framework yields a central limit theorem for shape parameters, too. This central limit theorem contains many of the previous central limit theorems from the literature and it can be used to prove recent conjectures and derive new results. As an example, we will consider a refinement of the size of tries and PATRICIA tries, namely, the number of nodes of fixed outdegree and obtain (univariate and bivariate) central limit theorems. Moreover, trivariate central limit theorems for size, internal path length and internal Wiener index of tries and PATRICIA tries are derived as well.
THE WIENER INDEX OF RANDOM DIGITAL TREES
(2015-01-01)
Fuchs, Michael
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Lee, Chung-Kuei
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應用數學系
;
Department of Applied Mathematics
The Wiener index has been studied for simply generated random trees, nonplane unlabeled random trees, and a huge subclass of random grid trees containing random binary search trees, random median-of-(2k+1) search trees, random m-ary search trees, random quadtrees, random simplex trees, etc. An important class of random grid trees for which the Wiener index was not studied so far is random digital trees. In this work, we close this gap. More precisely, we derive asymptotic expansions of moments of the Wiener index and show that a central limit law for the Wiener index holds. These results are obtained for digital search trees and bucket versions as well as tries and PATRICIA tries. Our findings answer in the affirmative two questions posed by Neininger.