The Probabilistic MethodPraise for the Second Edition: "Serious researchers in combinatorics or algorithm design will wish to read the book in its entirety...the book may also be enjoyed on a lighter level since the different chapters are largely independent and so it is possible to pick out gems in one's own area..." 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. 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:
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. |
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Inhoudsopgave
2 | |
Linearity of Expectation 2 1 Basics 2 2 Splitting Graphs 2 3 Two Quickies | |
The Second Moment | |
The Local | |
6 | |
Martingales and Tight Concentration | |
8 | |
Theory | |
Circuit Complexity | |
Discrepancy | |
Geometry | |
15 | |
Derandomization | |
Graph Property Testing | |
Boundingof Large Deviations | |