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The Probabilistic Method

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The Probabilistic Method

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Author : Noga Alon
language : en
Publisher: John Wiley & Sons
Release Date : 2004-03-22

The Probabilistic Method written by Noga Alon and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-22 with Mathematics categories.

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

The Probabilistic Method

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Author : Noga Alon
language : en
Publisher: John Wiley & Sons
Release Date : 2011-09-20

Praise 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..." —Formal Aspects of Computing 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: 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 Szemerédi Regularity Lemma and its applications New sections devoted to percolation and liar games A new chapter that provides a modern treatment of the Erdös-Rényi 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.

Ten Lectures On The Probabilistic Method

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Author : Joel Spencer
language : en
Publisher: SIAM
Release Date : 1994-01-01

Ten Lectures On The Probabilistic Method written by Joel Spencer and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-01-01 with Mathematics categories.

Ten Lectures On The Probabilistic Method

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Author : Joel H. Spencer
language : en
Publisher:
Release Date : 1987

Ten Lectures On The Probabilistic Method written by Joel H. Spencer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Combinatorial analysis categories.

Graph Colouring And The Probabilistic Method

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Author : Michael Molloy
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Graph Colouring And The Probabilistic Method written by Michael Molloy and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.

Over the past decade, many major advances have been made in the field of graph colouring via the probabilistic method. This monograph provides an accessible and unified treatment of these results, using tools such as the Lovasz Local Lemma and Talagrand's concentration inequality. The topics covered include: Kahn's proofs that the Goldberg-Seymour and List Colouring Conjectures hold asymptotically; a proof that for some absolute constant C, every graph of maximum degree Delta has a Delta+C total colouring; Johansson's proof that a triangle free graph has a O(Delta over log Delta) colouring; algorithmic variants of the Local Lemma which permit the efficient construction of many optimal and near-optimal colourings. This begins with a gentle introduction to the probabilistic method and will be useful to researchers and graduate students in graph theory, discrete mathematics, theoretical computer science and probability.

Ten Lectures On The Probabilistic Method

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Author : Joel Spencer
language : en
Publisher: SIAM
Release Date : 1994-01-01

This update of the 1987 title of the same name is an examination of what is currently known about the probabilistic method, written by one of its principal developers. Based on the notes from Spencer's 1986 series of ten lectures, this new edition contains an additional lecture: The Janson inequalities. These inequalities allow accurate approximation of extremely small probabilities. A new algorithmic approach to the Lovasz Local Lemma, attributed to Jozsef Beck, has been added to Lecture 8, as well. Throughout the monograph, Spencer retains the informal style of his original lecture notes and emphasizes the methodology, shunning the more technical "best possible" results in favor of clearer exposition. The book is not encyclopedic--it contains only those examples that clearly display the methodology. The probabilistic method is a powerful tool in graph theory, combinatorics, and theoretical computer science. It allows one to prove the existence of objects with certain properties (e.g., colorings) by showing that an appropriately defined random object has positive probability of having those properties.

Application Of A Probabilistic Method Based On Neutrosophic Number In Rock Slope Stability Assessment

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Author : Bo Li
language : en
Publisher: Infinite Study
Release Date :

Application Of A Probabilistic Method Based On Neutrosophic Number In Rock Slope Stability Assessment written by Bo Li and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.

The stability of natural rock slopes is influenced by a wide spectrum of factors, such as mechanical properties of bedrocks and spatial distribution of discontinuities. Their specific values are typically incomplete, due mainly to the lack of effective and comprehensive methods to accurately characterize these factors, especially those inside of the slopes. The neutrosophic number is a useful tool to solve problems in indeterminate environment.

Probabilistic Methods For Algorithmic Discrete Mathematics

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Author : Michel Habib
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Probabilistic Methods For Algorithmic Discrete Mathematics written by Michel Habib and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.

Leave nothing to chance. This cliche embodies the common belief that ran domness has no place in carefully planned methodologies, every step should be spelled out, each i dotted and each t crossed. In discrete mathematics at least, nothing could be further from the truth. Introducing random choices into algorithms can improve their performance. The application of proba bilistic tools has led to the resolution of combinatorial problems which had resisted attack for decades. The chapters in this volume explore and celebrate this fact. Our intention was to bring together, for the first time, accessible discus sions of the disparate ways in which probabilistic ideas are enriching discrete mathematics. These discussions are aimed at mathematicians with a good combinatorial background but require only a passing acquaintance with the basic definitions in probability (e.g. expected value, conditional probability). A reader who already has a firm grasp on the area will be interested in the original research, novel syntheses, and discussions of ongoing developments scattered throughout the book. Some of the most convincing demonstrations of the power of these tech niques are randomized algorithms for estimating quantities which are hard to compute exactly. One example is the randomized algorithm of Dyer, Frieze and Kannan for estimating the volume of a polyhedron. To illustrate these techniques, we consider a simple related problem. Suppose S is some region of the unit square defined by a system of polynomial inequalities: Pi (x. y) ~ o.

Probability And Computing

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Author : Michael Mitzenmacher
language : en
Publisher: Cambridge University Press
Release Date : 2005-01-31

Probability And Computing written by Michael Mitzenmacher and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-31 with Computers categories.

Randomization and probabilistic techniques play an important role in modern computer science, with applications ranging from combinatorial optimization and machine learning to communication networks and secure protocols. This 2005 textbook is designed to accompany a one- or two-semester course for advanced undergraduates or beginning graduate students in computer science and applied mathematics. It gives an excellent introduction to the probabilistic techniques and paradigms used in the development of probabilistic algorithms and analyses. It assumes only an elementary background in discrete mathematics and gives a rigorous yet accessible treatment of the material, with numerous examples and applications. The first half of the book covers core material, including random sampling, expectations, Markov's inequality, Chevyshev's inequality, Chernoff bounds, the probabilistic method and Markov chains. The second half covers more advanced topics such as continuous probability, applications of limited independence, entropy, Markov chain Monte Carlo methods and balanced allocations. With its comprehensive selection of topics, along with many examples and exercises, this book is an indispensable teaching tool.

Discrete Maths And Its Applications Global Edition 7e

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Author : Kenneth Rosen
language : en
Publisher: McGraw Hill
Release Date : 2012-09-16

Discrete Maths And Its Applications Global Edition 7e written by Kenneth Rosen and has been published by McGraw Hill this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-16 with Mathematics categories.

We are pleased to present this Global Edition which has been developed specifically to meet the needs of international students of discrete mathematics. In addition to great depth in key areas and a broad range of real-world applications across multiple disciplines, we have added new material to make the content more relevant and improve learning outcomes for the international student.This Global Edition includes: An entire new chapter on Algebraic Structures and Coding Theory New and expanded sections within chapters covering Foundations, Basic Structures, and Advanced Counting Techniques Special online only chapters on Boolean Algebra and Modeling Computation New and revised problems for the international student integrating alternative methods and solutions.This Global Edition has been adapted to meet the needs of courses outside of the United States and does not align with the instructor and student resources available with the US edition.

The Probabilistic Method

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