Discrete Probability And Algorithms
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Discrete Probability And Algorithms
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Author : David Aldous
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Discrete Probability And Algorithms written by David Aldous 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 2012-12-06 with Mathematics categories.
Discrete probability theory and the theory of algorithms have become close partners over the last ten years, though the roots of this partnership go back much longer. The papers in this volume address the latest developments in this active field. They are from the IMA Workshops "Probability and Algorithms" and "The Finite Markov Chain Renaissance." They represent the current thinking of many of the world's leading experts in the field. Researchers and graduate students in probability, computer science, combinatorics, and optimization theory will all be interested in this collection of articles. The techniques developed and surveyed in this volume are still undergoing rapid development, and many of the articles of the collection offer an expositionally pleasant entree into a research area of growing importance.
Computational Probability
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Author : John H. Drew
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-08
Computational Probability written by John H. Drew 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 2008-01-08 with Mathematics categories.
This title organizes computational probability methods into a systematic treatment. The book examines two categories of problems. "Algorithms for Continuous Random Variables" covers data structures and algorithms, transformations of random variables, and products of independent random variables. "Algorithms for Discrete Random Variables" discusses data structures and algorithms, sums of independent random variables, and order statistics.
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.
Randomization Methods In Algorithm Design
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Author : Panos M. Pardalos
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Randomization Methods In Algorithm Design written by Panos M. Pardalos and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Algorithms categories.
This volume is based on proceedings held during the DIMACS workshop on Randomization Methods in Algorithm Design in December 1997 at Princeton. The workshop was part of the DIMACS Special Year on Discrete Probability. It served as an interdisciplinary research workshop that brought together a mix of leading theorists, algorithmists and practitioners working in the theory and implementation aspects of algorithms involving randomization. Randomization has played an important role in the design of both sequential and parallel algorithms. The last decade has witnessed tremendous growth in the area of randomized algorithms. During this period, randomized algorithms went from being a tool in computational number theory to finding widespread applications in many problem domains. Major topics covered include randomization techniques for linear and integer programming problems, randomization in the design of approximate algorithms for combinatorial problems, randomization in parallel and distributed algorithms, practical implementation of randomized algorithms, de-randomization issues, and pseudo-random generators. This volume focuses on theory and implementation aspects of algorithms involving randomization. It would be suitable as a graduate or advanced graduate text.
Probability And Computing
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Author : Michael Mitzenmacher
language : en
Publisher:
Release Date : 2005
Probability And Computing written by Michael Mitzenmacher and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with 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 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, balls and bins models, the probabilistic method, and Markov chains. In the second half, the authors delve into more advanced topics such as continuous probability, applications of limited independence, entropy, Markov chain Monte Carlo methods, coupling, martingales, and balanced allocations. With its comprehensive selection of topics, along with many examples and exercises, this book is an indispensable teaching tool.
Probability And Statistics With Reliability Queuing And Computer Science Applications
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Author : KISHOR SHRIDHARBHAI TRIVEDI
language : en
Publisher: PHI Learning Pvt. Ltd.
Release Date : 1988-01-01
Probability And Statistics With Reliability Queuing And Computer Science Applications written by KISHOR SHRIDHARBHAI TRIVEDI and has been published by PHI Learning Pvt. Ltd. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-01-01 with Mathematics categories.
This book provides an introduction to probability, stochastic processes, and statistics for students of computer science, electrical/computer engineering, reliability engineering and applied mathematics. It prepares the student for solving practical stochastic modelling problems, and for the more advanced courses on queuing or reliability theory. The text emphasizes on applications, illustrating each theoretical concept by solved examples relating to algorithm analysis or communication related problems.The prerequisites are a knowledge of calculus, a course on introduction to computer programming, and an understanding of computer organization. The book is also suitable for self-study by computer professionals and mathematicians interested in applications.
Mathematics And Computer Science
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Author : Daniele Gardy
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Mathematics And Computer Science written by Daniele Gardy and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This is the first book where mathematics and computer science are directly confronted and joined to tackle intricate problems in computer science with deep mathematical approaches. It contains a collection of refereed papers presented at the Colloquium on Mathematics and Computer Science held at the University of Versailles-St-Quentin on September 18-20, 2000. The colloquium was a meeting place for researchers in mathematics and computer science and thus an important opportunity to exchange ideas and points of view, and to present new approaches and new results in the common areas such as algorithms analysis, trees, combinatorics, optimization, performance evaluation and probabilities. The book is intended for a large public in applied mathematics, discrete mathematics and computer science, including researchers, teachers, graduate students and engineers. It provides an overview of the current questions in computer science and related modern mathematical methods. The range of applications is very wide and reaches beyond computer science.
Discrete Mathematics For Computer Science
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Author : John Schlipf
language : en
Publisher:
Release Date : 2020-09-22
Discrete Mathematics For Computer Science written by John Schlipf and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-22 with categories.
Discrete Mathematics for Computer Science by Gary Haggard , John Schlipf , Sue Whitesides A major aim of this book is to help you develop mathematical maturity-elusive as thisobjective may be. We interpret this as preparing you to understand how to do proofs ofresults about discrete structures that represent concepts you deal with in computer science.A correct proof can be viewed as a set of reasoned steps that persuade another student,the course grader, or the instructor about the truth of the assertion. Writing proofs is hardwork even for the most experienced person, but it is a skill that needs to be developedthrough practice. We can only encourage you to be patient with the process. Keep tryingout your proofs on other students, graders, and instructors to gain the confidence that willhelp you in using proofs as a natural part of your ability to solve problems and understandnew material. The six chapters referred to contain the fundamental topics. Thesechapters are used to guide students in learning how to express mathematically precise ideasin the language of mathematics.The two chapters dealing with graph theory and combinatorics are also core materialfor a discrete structures course, but this material always seems more intuitive to studentsthan the formalism of the first four chapters. Topics from the first four chapters are freelyused in these later chapters. The chapter on discrete probability builds on the chapter oncombinatorics. The chapter on the analysis of algorithms uses notions from the core chap-ters but can be presented at an informal level to motivate the topic without spending a lot oftime with the details of the chapter. Finally, the chapter on recurrence relations primarilyuses the early material on induction and an intuitive understanding of the chapter on theanalysis of algorithms. The material in Chapters 1 through 4 deals with sets, logic, relations, and functions.This material should be mastered by all students. A course can cover this material at differ-ent levels and paces depending on the program and the background of the students whenthey take the course. Chapter 6 introduces graph theory, with an emphasis on examplesthat are encountered in computer science. Undirected graphs, trees, and directed graphsare studied. Chapter 7 deals with counting and combinatorics, with topics ranging from theaddition and multiplication principles to permutations and combinations of distinguishableor indistinguishable sets of elements to combinatorial identities.Enrichment topics such as relational databases, languages and regular sets, uncom-putability, finite probability, and recurrence relations all provide insights regarding howdiscrete structures describe the important notions studied and used in computer science.Obviously, these additional topics cannot be dealt with along with the all the core materialin a one-semester course, but the topics provide attractive alternatives for a variety of pro-grams. This text can also be used as a reference in courses. The many problems provideample opportunity for students to deal with the material presented.
Computational Probability
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Author : John H. Drew
language : en
Publisher: Springer
Release Date : 2016-12-15
Computational Probability written by John H. Drew and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-15 with Business & Economics categories.
This new edition includes the latest advances and developments in computational probability involving A Probability Programming Language (APPL). The book examines and presents, in a systematic manner, computational probability methods that encompass data structures and algorithms. The developed techniques address problems that require exact probability calculations, many of which have been considered intractable in the past. The book addresses the plight of the probabilist by providing algorithms to perform calculations associated with random variables. Computational Probability: Algorithms and Applications in the Mathematical Sciences, 2nd Edition begins with an introductory chapter that contains short examples involving the elementary use of APPL. Chapter 2 reviews the Maple data structures and functions necessary to implement APPL. This is followed by a discussion of the development of the data structures and algorithms (Chapters 3–6 for continuous random variables and Chapters 7–9 for discrete random variables) used in APPL. The book concludes with Chapters 10–15 introducing a sampling of various applications in the mathematical sciences. This book should appeal to researchers in the mathematical sciences with an interest in applied probability and instructors using the book for a special topics course in computational probability taught in a mathematics, statistics, operations research, management science, or industrial engineering department.
The Probabilistic Method
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Author : Noga Alon
language : en
Publisher: John Wiley & Sons
Release Date : 2015-11-02
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 2015-11-02 with Mathematics categories.
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.