Random Trees: An Interplay Between Combinatorics and Probability

ISBN-13: 9783211999141 / Angielski / Miękka / 2010 / 458 str.

Springer

Opis

Trees are a fundamental object in graph theory and combinatorics as well as a basic object for data structures and algorithms in computer science. During the last years research related to (random) trees has been constantly increasing and several asymptotic and probabilistic techniques have been developed in order to describe characteristics of interest of large trees in different settings.

The aim of this book is to provide a thorough introduction into various aspects of trees in random settings and a systematic treatment of the involved mathematical techniques. It should serve as a reference book as well as a basis for future research. One major conceptual aspect is to bridge combinatorial and probabilistic methods that range from counting techniques (generating functions, bijections) over asymptotic methods (saddle point techniques, singularity analysis) to various sophisticated techniques in asymptotic probability (martingales, convergence of stochastic processes, concentration inequalities).

Spis treści

Classes of Random Trees.- Generating Functions.- Advanced Tree Counting.- The Shape of Galton-Watson Trees and Pólya Trees.- The Vertical Profile of Trees.- Recursive Trees and Binary Search Trees.- Tries and Digital Search Trees.- Recursive Algorithms and the Contraction Method.- Planar Graphs.