The 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
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.
- Alon, Noga
- Spencer, Joel H.
- John Wiley and Sons, Inc.
- Publication year
- Wiley-Interscience Series in Discrete Mathematics and Optimization
- Page amount
- 384 pages
- Natural Sciences
- eISBN (ePUB)
- Printed ISBN