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rafik Amor Aguech

Associate Professor

عضو هيئة تدريس,

كلية العلوم
المبنى 4, الدور 1, رقم المكتب 2ب 44
المنشورات
ورقة مؤتمر
2005
تم النشر فى:

Distribution of Inter-Node Distances in Digital Trees

Mahmoud, Rafik Aguech, Nabil Lasmar, Hosam . 2005

Research paper

We investigate distances between pairs of nodes in digital trees (digital search trees (DST), and tries). By analytic techniques, such as the Mellin Transform and poissonization, we describe a program to determine the moments of these distances. The program is illustrated on the mean and variance. One encounters delayed Mellin transform equations, which we solve by inspection. Interestingly, the unbiased case gives a bounded variance, whereas the biased case gives a variance growing with the number of keys. It is therefore possible in the biased case to show that an appropriately normalized version of the distance converges to a limit. The complexity of moment calculation increases substantially with each higher moment; A shortcut to the limit is needed via a method that avoids the computation of all moments. Toward this end, we utilize the contraction method to show that in biased digital search trees the distribution of a suitably normalized version of the distances approaches a limit that is the fixed-point solution (in the Wasserstein space) of a distributional equation. An explicit solution to the fixed-point equation is readily demonstrated to be Gaussian. 

نوع عمل المنشور
Proceedings
موقع المؤتمر
DCMTCS
اسم المؤتمر
2005 International Conference on Analysis of Algorithms
المنظمة الممولة
INRIA France
مزيد من المنشورات
publications
بواسطة R. Aguech, S. Ilji
2021
publications
بواسطة R. Aguech,S. Bose, H. Mahmoud, Y. Zhang
2021