The Subtree Size Profile of Plane-oriented Recursive Trees

Fuchs, Michael

doi:10.1137/1.9781611973013.10

Cited by 3 publications

(3 citation statements)

References 28 publications

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“…These include the limit distribution of the normalized profile, asymptotic bimodality of the variance, asymptotic approximation to the expected width and the correlation coefficients of two level sizes. Fuchs [369] outlines how to derive limit theorems for the number of sub-trees of size k on the fringe of random plane-oriented recursive trees. Finally, Janson, Kuba and Panholzer [446] consider generalized Stirling permutations and relate them with certain families of generalized plane recursive trees.…”

Section: Inhomogeneous Recursive Trees Plane-oriented Recursive Treesmentioning

confidence: 99%

Introduction to Random Graphs

2015

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From social networks such as Facebook, the World Wide Web and the Internet, to the complex interactions between proteins in the cells of our bodies, we constantly face the challenge of understanding the structure and development of networks. The theory of random graphs provides a framework for this understanding, and in this book the authors give a gentle introduction to the basic tools for understanding and applying the theory. Part I includes sufficient material, including exercises, for a one semester course at the advanced undergraduate or beginning graduate level. The reader is then well prepared for the more advanced topics in Parts II and III. A final part provides a quick introduction to the background material needed. All those interested in discrete mathematics, computer science or applied probability and their applications will find this an ideal introduction to the subject.

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Section: Inhomogeneous Recursive Trees Plane-oriented Recursive Treesmentioning

confidence: 99%

Introduction to Random Graphs

2015

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“…in the asymmetric case, where G = Φ 1 + Φ 2 with Φ 1 , Φ 2 and d given below in (41), (43), and (42), respectively.…”

Section: External Path Lengthmentioning

confidence: 99%

“…Data Structures. Tries: [73,77,102]; PATRICIA tries: [61,73,101]; Quadtries and k-d tries: [32,43]; Hashing: [20,82,39,24]; Suffix trees: [60,102].…”

Section: Introductionmentioning

confidence: 99%

An analytic approach to the asymptotic variance of trie statistics and related structures

Fuchs

Hwang

Zacharovas

2014

Theoretical Computer Science

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We develop analytic tools for the asymptotics of general trie statistics, which are particularly advantageous for clarifying the asymptotic variance. Many concrete examples are discussed for which new Fourier expansions are given. The tools are also useful for other splitting processes with an underlying binomial distribution. We specially highlight Philippe Flajolet's contribution in the analysis of these random structures.

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Profile of Random Exponential Recursive Trees

Mahmoud

2021

Methodol Comput Appl Probab

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The Subtree Size Profile of Plane-oriented Recursive Trees

Cited by 3 publications

References 28 publications

Introduction to Random Graphs

Introduction to Random Graphs

An analytic approach to the asymptotic variance of trie statistics and related structures

Profile of Random Exponential Recursive Trees

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