The Probabilistic Method (Wiley Series in Discrete Mathematics and Optimization) - Hardcover

Alon, Noga; Spencer, Joel H.

Hardcover

ISBN 10: 0470170204 ISBN 13: 9780470170205

Publisher: Wiley–Blackwell, 2008

Synopsis

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.

About this title

Review

"...an exciting well–written book which will give much enjoyment to a reader..." (Mathematical Reviews, 2003f)

Synopsis

This Third Edition of "The Probabilistic Method" reflects the most recent developments in the field while maintaining the standard of excellence that established this book as the leading reference on probabilistic methods in combinatorics. Maintaining its clear writing style, illustrative examples, and practical exercises, this new edition emphasizes methodology, enabling readers to use probabilistic techniques for solving problems in such fields as theoretical computer science, mathematics, and statistical physics. This book begins with a description of tools applied in probabilistic arguments, including basic techniques that use expectation and variance as well as the more recent applications of martingales and correlation inequalities. Next, the authors examine where probabilistic techniques have been applied successfully, exploring such topics as discrepancy and random graphs, circuit complexity, computational geometry, and derandomization of randomized algorithms.Sections labeled 'The Probabilistic Lens' offer additional insights into the application of the probabilistic approach, and the appendix has been updated to include methodologies for finding lower bounds for Large Deviations.

The Third Edition also features: a new chapter on graph property testing, which is a current topic that incorporates combinatorial, probabilistic, and algorithmic techniques; an elementary approach using probabilistic techniques to the powerful Szemeredi Regularity Lemma and its applications; new sections devoted to percolation and liar games; and, a new chapter that provides a modern treatment of the Erdos-Renyi phase transition in the Random Graph Process.Written by two leading authorities in the field, "The Probabilistic Method, Third Edition" is an ideal reference for researchers in combinatorics and algorithm design who would like to better understand the use of probabilistic methods. The book's numerous exercises and examples also make it an excellent textbook for graduate-level courses in mathematics and computer science.

Edition details

• Publisher: Wiley–Blackwell
• Publication date: 2008
• ISBN 10: 0470170204
• ISBN 13: 9780470170205
• Binding: Hardcover
• Language: English
• Edition number: 3
• Number of pages: 376