Overview

One of the most powerful and popular tools used in combinatorics is the probabilistic method. Describes current algorithmic techniques, applying both the classical method and the modern tools it uses. Along with a detailed description of the techniques used in probabilistic arguments, it includes basic methods which utilize expectation and variance plus recent applications of martingales and correlation inequalities. Examines discrepancy and random graphs and covers such topics as theoretical computer science, ...
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The Probabilistic Method

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Overview

One of the most powerful and popular tools used in combinatorics is the probabilistic method. Describes current algorithmic techniques, applying both the classical method and the modern tools it uses. Along with a detailed description of the techniques used in probabilistic arguments, it includes basic methods which utilize expectation and variance plus recent applications of martingales and correlation inequalities. Examines discrepancy and random graphs and covers such topics as theoretical computer science, computational geometry, derandomization of randomized algorithms and more. A study of various topics using successful probabilistic techniques is included along with an Open Problems Appendix by Paul Erdos, the founder of the probabilistic method.
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Editorial Reviews

Booknews
The probabilistic method has undergone intensive development in the wake of the increasing significance of randomness in theoretical computer science. This text features detailed descriptions of algorithmic techniques combined with a study of the classical method and the modern tools commonly applied in it. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9781118210444
  • Publisher: Wiley, John & Sons, Incorporated
  • Publication date: 9/20/2011
  • Series: Wiley Series in Discrete Mathematics and Optimization , #73
  • Sold by: Barnes & Noble
  • Format: eBook
  • Edition number: 3
  • Pages: 376
  • File size: 20 MB
  • Note: This product may take a few minutes to download.

Meet the Author

NOGA ALON, PhD, is Baumritter Professor of Mathematics and Computer Science at Tel Aviv University, Israel. A member of the Israel National Academy of Sciences, Dr. Alon has written over 400 published papers, mostly in the areas of combinatorics and theoretical computer science. He is the recipient of numerous honors in the field, including the Erdös Prize (1989), the Pólya Prize (2000), the Landau Prize (2005), and the Gödel Prize (2005).

JOEL H. SPENCER, PhD, is Professor of Mathematics and Computer Science at the Courant Institute of Mathematical Sciences at New York University and is the cofounder and coeditor of the journal Random Structures and Algorithms. Dr. Spencer has written over 150 published articles and is the coauthor of Ramsey Theory, Second Edition, also published by Wiley.

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Table of Contents

Dedication
Preface
Acknowledgments
Pt. I Methods
1 The Basic Method
The Probabilistic Lens: The Erdos-Ko-Rado Theorem
2 Linearity of Expectation
The Probabilistic Lens: Bregman's Theorem
3 Alterations
The Probabilistic Lens: High Girth and High Chromatic Number
4 The Second Moment
The Probabilistic Lens: Hamiltonian Paths
5 The Local Lemma
The Probabilistic Lens: Directed Cycles
6 Correlation Inequalities
The Probabilistic Lens: Turan's Theorem
7 Martingales and Tight Concentration
The Probabilistic Lens: Weierstrass Approximation Theorem
8 The Poisson Paradigm
The Probabilistic Lens: Local Coloring
9 Pseudorandomness
The Probabilistic Lens: Random Walks
Pt. II Topics
10 Random Graphs
The Probabilistic Lens: Counting Subgraphs
11 Circuit Complexity
The Probabilistic Lens: Maximal Antichains
12 Discrepancy
The Probabilistic Lens: Unbalancing Lights
13 Geometry
The Probabilistic Lens: Efficient Packing
14 Codes, Games and Entropy
The Probabilistic Lens: An Extremal Graph
15 Derandomization
The Probabilistic Lens: Crossing Numbers, Incidences, Sums and Products
App. A Bounding of Large Deviations
The Probabilistic Lens: Triangle-free Graphs Have Large Independence Numbers
App. B Paul Erdos
References
Subject Index
Author Index
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