Analytic Combinatorics Flajolet
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Analytic Combinatorics
Author: Philippe Flajolet
language: en
Publisher: Cambridge University Press
Release Date: 2009-01-15
Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.
From Analysis of Algorithms to Analytic Combinatorics
"Analysis of Algorithms Video Lectures cover the essential information that every serious programmer needs to know about analyzing algorithms, including analytic combinatorics. In these videos, basic coverage of recurrences, generating functions, and asymptotics leads to an introduction to analytic combinatorics, including labeled and unlabeled combinatorial classes. The videos go on to cover survey trees, permutations, strings and tries, and words and mappings, with applications drawn from the study of widely-used algorithms. This collection of video lectures provides an introductory exploration of how to mathematically analyze algorithms. Author Robert Sedgewick emphasizes the mathematics required to support scientific studies that can serve as the basis for predicting algorithms and for comparing different algorithms on the basis of performance. Every lecture is accompanied with suggested related readings that you can find in An Introduction to the Analysis of Algorithms, Second Edition. These lectures provide another perspective on the material presented in the book and are in one-to-one correspondence with the chapters in the textbook."--Resource description page.
An Introduction to the Analysis of Algorithms
Despite growing interest, basic information on methods and models for mathematically analyzing algorithms has rarely been directly accessible to practitioners, researchers, or students. An Introduction to the Analysis of Algorithms, Second Edition, organizes and presents that knowledge, fully introducing primary techniques and results in the field. Robert Sedgewick and the late Philippe Flajolet have drawn from both classical mathematics and computer science, integrating discrete mathematics, elementary real analysis, combinatorics, algorithms, and data structures. They emphasize the mathematics needed to support scientific studies that can serve as the basis for predicting algorithm performance and for comparing different algorithms on the basis of performance. Techniques covered in the first half of the book include recurrences, generating functions, asymptotics, and analytic combinatorics. Structures studied in the second half of the book include permutations, trees, strings, tries, and mappings. Numerous examples are included throughout to illustrate applications to the analysis of algorithms that are playing a critical role in the evolution of our modern computational infrastructure. Improvements and additions in this new edition include Upgraded figures and code An all-new chapter introducing analytic combinatorics Simplified derivations via analytic combinatorics throughout The book’s thorough, self-contained coverage will help readers appreciate the field’s challenges, prepare them for advanced results—covered in their monograph Analytic Combinatorics and in Donald Knuth’s The Art of Computer Programming books—and provide the background they need to keep abreast of new research. "[Sedgewick and Flajolet] are not only worldwide leaders of the field, they also are masters of exposition. I am sure that every serious computer scientist will find this book rewarding in many ways." —From the Foreword by Donald E. Knuth