Download or read book Algorithmic Probability and Combinatorics written by Manuel Lladser and published by American Mathematical Soc.. This book was released on 2010-07-30 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS Special Sessions on Algorithmic Probability and Combinatories held at DePaul University on October 5-6, 2007 and at the University of British Columbia on October 4-5, 2008. This volume collects cutting-edge research and expository on algorithmic probability and combinatories. It includes contributions by well-established experts and younger researchers who use generating functions, algebraic and probabilistic methods as well as asymptotic analysis on a daily basis. Walks in the quarter-plane and random walks (quantum, rotor and self-avoiding), permutation tableaux, and random permutations are considered. In addition, articles in the volume present a variety of saddle-point and geometric methods for the asymptotic analysis of the coefficients of single-and multivariable generating functions associated with combinatorial objects and discrete random structures. The volume should appeal to pure and applied mathematicians, as well as mathematical physicists; in particular, anyone interested in computational aspects of probability, combinatories and enumeration. Furthermore, the expository or partly expository papers included in this volume should serve as an entry point to this literature not only to experts in other areas, but also to graduate students.
Download or read book Algorithmic Probability written by Marcel F. Neuts and published by CRC Press. This book was released on 1995-07-01 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique text collects more than 400 problems in combinatorics, derived distributions, discrete and continuous Markov chains, and models requiring a computer experimental approach. The first book to deal with simplified versions of models encountered in the contemporary statistical or engineering literature, Algorithmic Probability emphasizes correct interpretation of numerical results and visualization of the dynamics of stochastic processes. A significant contribution to the field of applied probability, Algorithmic Probability is ideal both as a secondary text in probability courses and as a reference. Engineers and operations analysts seeking solutions to practical problems will find it a valuable resource, as will advanced undergraduate and graduate students in mathematics, statistics, operations research, industrial and electrical engineering, and computer science.
Download or read book Mathematics and Computer Science written by Daniele Gardy and published by Birkhäuser. This book was released on 2012-12-06 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Download or read book Random Trees written by Michael Drmota and published by Springer Science & Business Media. This book was released on 2009-04-16 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to provide a thorough introduction to various aspects of trees in random settings and a systematic treatment of the mathematical analysis techniques involved. It should serve as a reference book as well as a basis for future research.
Download or read book Combinatorics and Probability written by Graham Brightwell and published by Cambridge University Press. This book was released on 2007-03-08 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume celebrating the 60th birthday of Béla Bollobás presents the state of the art in combinatorics.
Download or read book Mathematics and Computer Science II written by Brigitte Chauvin and published by Birkhäuser. This book was released on 2012-12-06 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second volume in a series of innovative proceedings entirely devoted to the connections between mathematics and computer science. Here mathematics and computer science are directly confronted and joined to tackle intricate problems in computer science with deep and innovative mathematical approaches. The book serves as an outstanding tool and a main information source 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 the related modern and powerful mathematical methods. The range of applications is very wide and reaches beyond computer science.
Download or read book Discrete Probability and Algorithms written by David Aldous and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Probability Combinatorics and Control written by Andrey Kostogryzov and published by BoD – Books on Demand. This book was released on 2020-04-15 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probabilistic and combinatorial techniques are often used for solving advanced problems. This book describes different probabilistic modeling methods and their applications in various areas, such as artificial intelligence, offshore platforms, social networks, and others. It aims to educate how modern probabilistic and combinatorial models may be created to formalize uncertainties; to train how new probabilistic models can be generated for the systems of complex structures; to describe the correct use of the presented models for rational control in systems creation and operation; and to demonstrate analytical possibilities and practical effects for solving different system problems on each life cycle stage.
Download or read book Analytic Combinatorics written by Philippe Flajolet and published by Cambridge University Press. This book was released on 2009-01-15 with total page 825 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.
Download or read book Combinatorics Algorithms Probabilistic and Experimental Methodologies written by Bo Chen and published by Springer Science & Business Media. This book was released on 2007-09-28 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: The First International Symposium on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies was held in Hangzhou, China, in April 2007. The symposium provided an interdisciplinary forum for researchers to share their discoveries and approaches; search for ideas, methodologies, and tool boxes; find better, faster, and more accurate solutions; and develop a research agenda of common interest. This volume constitutes the refereed post-proceedings of the symposium. Inside you'll find 46 full papers. They represent some of the most important thinking and advancements in the field. The papers address large data processing problems using different methodologies from major disciplines such as computer science, combinatorics, and statistics.
Download or read book The Probabilistic Method written by Noga Alon and published by John Wiley & Sons. This book was released on 2004-04-05 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Probability Theory and Combinatorial Optimization written by J. Michael Steele and published by SIAM. This book was released on 1997-01-01 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the state of the art of the probability theory most applicable to combinatorial optimization. The questions that receive the most attention are those that deal with discrete optimization problems for points in Euclidean space, such as the minimum spanning tree, the traveling-salesman tour, and minimal-length matchings.
Download or read book Ten Lectures on the Probabilistic Method written by Joel Spencer and published by SIAM. This book was released on 1994-01-01 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Algorithmics of Nonuniformity written by Micha Hofri and published by CRC Press. This book was released on 2018-07-16 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algorithmics of Nonuniformity is a solid presentation about the analysis of algorithms, and the data structures that support them. Traditionally, algorithmics have been approached either via a probabilistic view or an analytic approach. The authors adopt both approaches and bring them together to get the best of both worlds and benefit from the advantage of each approach. The text examines algorithms that are designed to handle general data—sort any array, find the median of any numerical set, and identify patterns in any setting. At the same time, it evaluates "average" performance, "typical" behavior, or in mathematical terms, the expectations of the random variables that describe their operations. Many exercises are presented, which are essential since they convey additional material complementing the content of the chapters. For this reason, the solutions are more than mere answers, but explain and expand upon related concepts, and motivate further work by the reader. Highlights: A unique book that merges probability with analysis of algorithms Approaches analysis of algorithms from the angle of uniformity Non-uniformity makes more realistic models of real-life scenarios possible Results can be applied to many applications Includes many exercises of various levels of difficulty About the Authors: Micha Hofri is a Professor of Computer Science, and former department head at Worcester Polytechnic Institute. He holds a Ph.D. of Industrial Engineering (1972), all from Technion, the Israel Institute of Technology. He has 39 publications in Mathematics. Hosam Mahmoud is a Professor at, the Department of Statistics at George Washington University in Washington D.C., where he used to be the former chair. He holds an Ph.D. in Computer Science from Ohio State University. He is on the editorial board of five academic journals.
Download or read book Geometric Algorithms and Combinatorial Optimization written by Martin Grötschel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Historically, there is a close connection between geometry and optImization. This is illustrated by methods like the gradient method and the simplex method, which are associated with clear geometric pictures. In combinatorial optimization, however, many of the strongest and most frequently used algorithms are based on the discrete structure of the problems: the greedy algorithm, shortest path and alternating path methods, branch-and-bound, etc. In the last several years geometric methods, in particular polyhedral combinatorics, have played a more and more profound role in combinatorial optimization as well. Our book discusses two recent geometric algorithms that have turned out to have particularly interesting consequences in combinatorial optimization, at least from a theoretical point of view. These algorithms are able to utilize the rich body of results in polyhedral combinatorics. The first of these algorithms is the ellipsoid method, developed for nonlinear programming by N. Z. Shor, D. B. Yudin, and A. S. NemirovskiI. It was a great surprise when L. G. Khachiyan showed that this method can be adapted to solve linear programs in polynomial time, thus solving an important open theoretical problem. While the ellipsoid method has not proved to be competitive with the simplex method in practice, it does have some features which make it particularly suited for the purposes of combinatorial optimization. The second algorithm we discuss finds its roots in the classical "geometry of numbers", developed by Minkowski. This method has had traditionally deep applications in number theory, in particular in diophantine approximation.
Download or read book The Probabilistic Method written by Noga Alon and published by John Wiley & Sons. This book was released on 2015-11-02 with total page 396 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.
