The Probabilistic Method - Couverture rigide

Alon, Noga; Etc.; Spencer, J.; Erdos, P.

Couverture rigide

ISBN 10 : 0471535885 ISBN 13 : 9780471535881

Editeur : John Wiley & Sons Inc, 1991

Synopsis

This a a guide to the probabilistic method, an extremely powerful tool for solving complex problems in discrete mathematics which is recognized as a primary methodology in theoretical computer science. Improved techniques and classical methods are discussed, with applications to discrete maths, theoretical computer science, circuit complexity, coding theory and computational geometry. The book also presents the probabilistic method in action and provides a section giving new insights into already known theorems and results.

A propos du livre

Présentation de l'éditeur

Praise for the Second Edition:

"Serious researchers in combinatorics or algorithm design willwish to read the book in its entirety...the book may also beenjoyed on a lighter level since the different chapters are largelyindependent and so it is possible to pick out gems in one′s ownarea..."
Formal Aspects of Computing

This Third Edition of The Probabilistic Method reflectsthe most recent developments in the field while maintaining thestandard of excellence that established this book as the leadingreference on probabilistic methods in combinatorics. Maintainingits clear writing style, illustrative examples, and practicalexercises, this new edition emphasizes methodology, enablingreaders to use probabilistic techniques for solving problems insuch fields as theoretical computer science, mathematics, andstatistical physics.

The book begins with a description of tools applied inprobabilistic arguments, including basic techniques that useexpectation and variance as well as the more recent applications ofmartingales and correlation inequalities. Next, the authors examinewhere probabilistic techniques have been applied successfully,exploring such topics as discrepancy and random graphs, circuitcomplexity, computational geometry, and derandomization ofrandomized algorithms. Sections labeled "The Probabilistic Lens"offer additional insights into the application of the probabilisticapproach, and the appendix has been updated to includemethodologies for finding lower bounds for Large Deviations.

The Third Edition also features:

• A new chapter on graph property testing, which is a currenttopic that incorporates combinatorial, probabilistic, andalgorithmic techniques

• An elementary approach using probabilistic techniques to thepowerful Szemerédi Regularity Lemma and its applications

• New sections devoted to percolation and liar games

• A new chapter that provides a modern treatment of theErdös–Rényi phase transition in the Random GraphProcess

Written by two leading authorities in the field, TheProbabilistic Method, Third Edition is an ideal reference forresearchers in combinatorics and algorithm design who would like tobetter understand the use of probabilistic methods. The book′snumerous exercises and examples also make it an excellent textbookfor graduate–level courses in mathematics and computer science.

Présentation de l'éditeur

The leading reference on probabilistic methods in combinatorics–now expanded and updated When it was first published in 1991, The Probabilistic Method became instantly the standard reference on one of the most powerful and widely used tools in combinatorics. Still without competition nearly a decade later, this new edition brings you up to speed on recent developments, while adding useful exercises and over 30% new material. It continues to emphasize the basic elements of the methodology, discussing in a remarkably clear and informal style both algorithmic and classical methods as well as modern applications. The Probabilistic Method, Second Edition begins with basic techniques that use expectation and variance, as well as the more recent martingales and correlation inequalities, then explores areas where probabilistic techniques proved successful, including discrepancy and random graphs as well as cutting–edge topics in theoretical computer science. A series of proofs, or "probabilistic lenses," are interspersed throughout the book, offering added insight into the application of the probabilistic approach. New and revised coverage includes: ∗ Several improved as well as new results ∗ A continuous approach to discrete probabilistic problems ∗ Talagrand′s Inequality and other novel concentration results ∗ A discussion of the connection between discrepancy and VC–dimension ∗ Several combinatorial applications of the entropy function and its properties ∗ A new section on the life and work of Paul Erdös–the developer of the probabilistic method

Détails de l'édition

• Éditeur: John Wiley & Sons Inc
• Date d'édition: 1991
• Langue: anglais
• ISBN 10: 0471535885
• ISBN 13: 9780471535881
• Reliure: Relié
• Nombre de pages: 272
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible