Probabilistic Methods In Discrete Mathematics

Author : Michel Habib
Publisher : Springer Science & Business Media
ISBN 13 : 3662127881
Total Pages : 342 pages
Book Rating : 4.89/5 ( download)

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Download or read book Probabilistic Methods for Algorithmic Discrete Mathematics written by Michel Habib and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Noga Alon
Publisher : John Wiley & Sons
ISBN 13 : 1119061962
Total Pages : 400 pages
Book Rating : 4.60/5 ( download)

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Download or read book The Probabilistic Method written by Noga Alon and published by John Wiley & Sons. This book was released on 2015-10-28 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the Third Edition “Researchers of any kind of extremal combinatorics or theoretical computer science will welcome the new edition of this book.” - MAA Reviews Maintaining a standard of excellence that establishes The Probabilistic Method as the leading reference on probabilistic methods in combinatorics, the Fourth Edition continues to feature a clear writing style, illustrative examples, and illuminating exercises. The new edition includes numerous updates to reflect the most recent developments and advances in discrete mathematics and the connections to other areas in mathematics, theoretical computer science, and statistical physics. Emphasizing the methodology and techniques that enable problem-solving, The Probabilistic Method, Fourth Edition begins with a description of tools applied to probabilistic arguments, including basic techniques that use expectation and variance as well as the more advanced applications of martingales and correlation inequalities. The authors explore where probabilistic techniques have been applied successfully and also examine topical coverage such as discrepancy and random graphs, circuit complexity, computational geometry, and derandomization of randomized algorithms. Written by two well-known authorities in the field, the Fourth Edition features: Additional exercises throughout with hints and solutions to select problems in an appendix to help readers obtain a deeper understanding of the best methods and techniques New coverage on topics such as the Local Lemma, Six Standard Deviations result in Discrepancy Theory, Property B, and graph limits Updated sections to reflect major developments on the newest topics, discussions of the hypergraph container method, and many new references and improved results The Probabilistic Method, Fourth Edition is an ideal textbook for upper-undergraduate and graduate-level students majoring in mathematics, computer science, operations research, and statistics. The Fourth Edition is also an excellent reference for researchers and combinatorists who use probabilistic methods, discrete mathematics, and number theory. Noga Alon, PhD, is Baumritter Professor of Mathematics and Computer Science at Tel Aviv University. He is a member of the Israel National Academy of Sciences and Academia Europaea. A coeditor of the journal Random Structures and Algorithms, Dr. Alon is the recipient of the Polya Prize, The Gödel Prize, The Israel Prize, and the EMET Prize. Joel H. Spencer, PhD, is Professor of Mathematics and Computer Science at the Courant Institute of New York University. He is the cofounder and coeditor of the journal Random Structures and Algorithms and is a Sloane Foundation Fellow. Dr. Spencer has written more than 200 published articles and is the coauthor of Ramsey Theory, Second Edition, also published by Wiley.

Author : Noga Alon
Publisher : John Wiley & Sons
ISBN 13 : 1118210441
Total Pages : 257 pages
Book Rating : 4.44/5 ( download)

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Download or read book The Probabilistic Method written by Noga Alon and published by John Wiley & Sons. This book was released on 2011-09-20 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Michael Molloy
Publisher : Springer Science & Business Media
ISBN 13 : 3642040160
Total Pages : 320 pages
Book Rating : 4.60/5 ( download)

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Download or read book Graph Colouring and the Probabilistic Method written by Michael Molloy and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past decade, many major advances have been made in the field of graph coloring via the probabilistic method. This monograph, by two of the best on the topic, provides an accessible and unified treatment of these results, using tools such as the Lovasz Local Lemma and Talagrand's concentration inequality.

Author : Brill Academic
Publisher :
ISBN 13 : 9780000023704
Total Pages : pages
Book Rating : 4.01/5 ( download)

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Download or read book Probabilistic Methods in Discrete Mathematics written by Brill Academic and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : V. F. Kolchin
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3112314077
Total Pages : 380 pages
Book Rating : 4.74/5 ( download)

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Download or read book Probabilistic Methods in Discrete Mathematics written by V. F. Kolchin and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-05-18 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Probabilistic Methods in Discrete Mathematics".

Author : Pierre Brémaud
Publisher : Springer
ISBN 13 : 3319434764
Total Pages : 561 pages
Book Rating : 4.66/5 ( download)

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Download or read book Discrete Probability Models and Methods written by Pierre Brémaud and published by Springer. This book was released on 2017-01-31 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: The emphasis in this book is placed on general models (Markov chains, random fields, random graphs), universal methods (the probabilistic method, the coupling method, the Stein-Chen method, martingale methods, the method of types) and versatile tools (Chernoff's bound, Hoeffding's inequality, Holley's inequality) whose domain of application extends far beyond the present text. Although the examples treated in the book relate to the possible applications, in the communication and computing sciences, in operations research and in physics, this book is in the first instance concerned with theory. The level of the book is that of a beginning graduate course. It is self-contained, the prerequisites consisting merely of basic calculus (series) and basic linear algebra (matrices). The reader is not assumed to be trained in probability since the first chapters give in considerable detail the background necessary to understand the rest of the book.

Author : V. F. Kolchin
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3112314107
Total Pages : 400 pages
Book Rating : 4.04/5 ( download)

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Download or read book Probabilistic Methods in Discrete Mathematics written by V. F. Kolchin and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-05-18 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Probabilistic Methods in Discrete Mathematics".

Author : Valentin Fedorovič Kolčin
Publisher : VSP
ISBN 13 : 9789067641586
Total Pages : 484 pages
Book Rating : 4.88/5 ( download)

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Download or read book Probabilistic Methods in Discrete Mathematics written by Valentin Fedorovič Kolčin and published by VSP. This book was released on 1993 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Michael Mitzenmacher
Publisher : Cambridge University Press
ISBN 13 : 9780521835404
Total Pages : 372 pages
Book Rating : 4.02/5 ( download)

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Download or read book Probability and Computing written by Michael Mitzenmacher and published by Cambridge University Press. This book was released on 2005-01-31 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.