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Combinatorial Methods And Models
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Book Synopsis Combinatorial Methods with Computer Applications by : Jonathan L. Gross
Download or read book Combinatorial Methods with Computer Applications written by Jonathan L. Gross and published by CRC Press. This book was released on 2016-04-19 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: This combinatorics text provides in-depth coverage of recurrences, generating functions, partitions, and permutations, along with some of the most interesting graph and network topics, design constructions, and finite geometries. It presents the computer and software algorithms in pseudo-code and incorporates definitions, theorems, proofs, examples, and nearly 300 illustrations as pedagogical elements of the exposition. Numerous problems, solutions, and hints reinforce basic skills and assist with creative problem solving. The author also offers a website with extensive graph theory informational resources as well as a computational engine to help with calculations for some of the exercises.
Book Synopsis Combinatorial Physics by : Adrian Tanasa
Download or read book Combinatorial Physics written by Adrian Tanasa and published by Oxford University Press. This book was released on 2021 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the book is to use combinatorial techniques to solve fundamental physics problems, and vice-versa, to use theoretical physics techniques to solve combinatorial problems.
Book Synopsis Introduction to Combinatorial Testing by : D. Richard Kuhn
Download or read book Introduction to Combinatorial Testing written by D. Richard Kuhn and published by CRC Press. This book was released on 2016-04-19 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial testing of software analyzes interactions among variables using a very small number of tests. This advanced approach has demonstrated success in providing strong, low-cost testing in real-world situations. Introduction to Combinatorial Testing presents a complete self-contained tutorial on advanced combinatorial testing methods for re
Book Synopsis Combinatorial Methods in Density Estimation by : Luc Devroye
Download or read book Combinatorial Methods in Density Estimation written by Luc Devroye and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: Density estimation has evolved enormously since the days of bar plots and histograms, but researchers and users are still struggling with the problem of the selection of the bin widths. This book is the first to explore a new paradigm for the data-based or automatic selection of the free parameters of density estimates in general so that the expected error is within a given constant multiple of the best possible error. The paradigm can be used in nearly all density estimates and for most model selection problems, both parametric and nonparametric.
Book Synopsis Analytic Combinatorics by : Philippe Flajolet
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.
Book Synopsis Combinatorial Methods in Discrete Mathematics by : Vladimir N. Sachkov
Download or read book Combinatorial Methods in Discrete Mathematics written by Vladimir N. Sachkov and published by Cambridge University Press. This book was released on 1996-01-11 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an attempt to present some complex problems of discrete mathematics in a simple and unified form using a unique, general combinatorial scheme. The author's aim is not always to present the most general results, but rather to focus attention on ones that illustrate the methods described. A distinctive aspect of the book is the large number of asymptotic formulae derived.This is an important book, describing many ideas not previously available in English; the author has taken the chance to update the text and references where appropriate.
Book Synopsis Model Theoretic Methods in Finite Combinatorics by : Martin Grohe
Download or read book Model Theoretic Methods in Finite Combinatorics written by Martin Grohe and published by American Mathematical Soc.. This book was released on 2011-11-28 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS-ASL Special Session on Model Theoretic Methods in Finite Combinatorics, held January 5-8, 2009, in Washington, DC. Over the last 20 years, various new connections between model theory and finite combinatorics emerged. The best known of these are in the area of 0-1 laws, but in recent years other very promising interactions between model theory and combinatorics have been developed in areas such as extremal combinatorics and graph limits, graph polynomials, homomorphism functions and related counting functions, and discrete algorithms, touching the boundaries of computer science and statistical physics. This volume highlights some of the main results, techniques, and research directions of the area. Topics covered in this volume include recent developments on 0-1 laws and their variations, counting functions defined by homomorphisms and graph polynomials and their relation to logic, recurrences and spectra, the logical complexity of graphs, algorithmic meta theorems based on logic, universal and homogeneous structures, and logical aspects of Ramsey theory.
Book Synopsis Multi-Objective Combinatorial Optimization Problems and Solution Methods by : Mehdi Toloo
Download or read book Multi-Objective Combinatorial Optimization Problems and Solution Methods written by Mehdi Toloo and published by Academic Press. This book was released on 2022-02-09 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multi-Objective Combinatorial Optimization Problems and Solution Methods discusses the results of a recent multi-objective combinatorial optimization achievement that considered metaheuristic, mathematical programming, heuristic, hyper heuristic and hybrid approaches. In other words, the book presents various multi-objective combinatorial optimization issues that may benefit from different methods in theory and practice. Combinatorial optimization problems appear in a wide range of applications in operations research, engineering, biological sciences and computer science, hence many optimization approaches have been developed that link the discrete universe to the continuous universe through geometric, analytic and algebraic techniques. This book covers this important topic as computational optimization has become increasingly popular as design optimization and its applications in engineering and industry have become ever more important due to more stringent design requirements in modern engineering practice. - Presents a collection of the most up-to-date research, providing a complete overview of multi-objective combinatorial optimization problems and applications - Introduces new approaches to handle different engineering and science problems, providing the field with a collection of related research not already covered in the primary literature - Demonstrates the efficiency and power of the various algorithms, problems and solutions, including numerous examples that illustrate concepts and algorithms
Book Synopsis Iterative Methods in Combinatorial Optimization by : Lap Chi Lau
Download or read book Iterative Methods in Combinatorial Optimization written by Lap Chi Lau and published by Cambridge University Press. This book was released on 2011-04-18 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the advent of approximation algorithms for NP-hard combinatorial optimization problems, several techniques from exact optimization such as the primal-dual method have proven their staying power and versatility. This book describes a simple and powerful method that is iterative in essence and similarly useful in a variety of settings for exact and approximate optimization. The authors highlight the commonality and uses of this method to prove a variety of classical polyhedral results on matchings, trees, matroids and flows. The presentation style is elementary enough to be accessible to anyone with exposure to basic linear algebra and graph theory, making the book suitable for introductory courses in combinatorial optimization at the upper undergraduate and beginning graduate levels. Discussions of advanced applications illustrate their potential for future application in research in approximation algorithms.
Book Synopsis Combinatorics of Genome Rearrangements by : Guillaume Fertin
Download or read book Combinatorics of Genome Rearrangements written by Guillaume Fertin and published by MIT Press. This book was released on 2009 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive survey of a rapidly expanding field of combinatorial optimization, mathematically oriented but offering biological explanations when required. From one cell to another, from one individual to another, and from one species to another, the content of DNA molecules is often similar. The organization of these molecules, however, differs dramatically, and the mutations that affect this organization are known as genome rearrangements. Combinatorial methods are used to reconstruct putative rearrangement scenarios in order to explain the evolutionary history of a set of species, often formalizing the evolutionary events that can explain the multiple combinations of observed genomes as combinatorial optimization problems. This book offers the first comprehensive survey of this rapidly expanding application of combinatorial optimization. It can be used as a reference for experienced researchers or as an introductory text for a broader audience. Genome rearrangement problems have proved so interesting from a combinatorial point of view that the field now belongs as much to mathematics as to biology. This book takes a mathematically oriented approach, but provides biological background when necessary. It presents a series of models, beginning with the simplest (which is progressively extended by dropping restrictions), each constructing a genome rearrangement problem. The book also discusses an important generalization of the basic problem known as the median problem, surveys attempts to reconstruct the relationships between genomes with phylogenetic trees, and offers a collection of summaries and appendixes with useful additional information.
Book Synopsis Geometric Algorithms and Combinatorial Optimization by : Martin Grötschel
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.
Book Synopsis Boolean Models and Methods in Mathematics, Computer Science, and Engineering by : Yves Crama
Download or read book Boolean Models and Methods in Mathematics, Computer Science, and Engineering written by Yves Crama and published by Cambridge University Press. This book was released on 2010-06-28 with total page 781 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of papers written by prominent experts that examine a variety of advanced topics related to Boolean functions and expressions.
Book Synopsis Distributed Computing Through Combinatorial Topology by : Maurice Herlihy
Download or read book Distributed Computing Through Combinatorial Topology written by Maurice Herlihy and published by Newnes. This book was released on 2013-11-30 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: Distributed Computing Through Combinatorial Topology describes techniques for analyzing distributed algorithms based on award winning combinatorial topology research. The authors present a solid theoretical foundation relevant to many real systems reliant on parallelism with unpredictable delays, such as multicore microprocessors, wireless networks, distributed systems, and Internet protocols. Today, a new student or researcher must assemble a collection of scattered conference publications, which are typically terse and commonly use different notations and terminologies. This book provides a self-contained explanation of the mathematics to readers with computer science backgrounds, as well as explaining computer science concepts to readers with backgrounds in applied mathematics. The first section presents mathematical notions and models, including message passing and shared-memory systems, failures, and timing models. The next section presents core concepts in two chapters each: first, proving a simple result that lends itself to examples and pictures that will build up readers' intuition; then generalizing the concept to prove a more sophisticated result. The overall result weaves together and develops the basic concepts of the field, presenting them in a gradual and intuitively appealing way. The book's final section discusses advanced topics typically found in a graduate-level course for those who wish to explore further. - Named a 2013 Notable Computer Book for Computing Methodologies by Computing Reviews - Gathers knowledge otherwise spread across research and conference papers using consistent notations and a standard approach to facilitate understanding - Presents unique insights applicable to multiple computing fields, including multicore microprocessors, wireless networks, distributed systems, and Internet protocols - Synthesizes and distills material into a simple, unified presentation with examples, illustrations, and exercises
Book Synopsis Methods And Models In Statistics: In Honour Of Professor John Nelder, Frs by : David J Hand
Download or read book Methods And Models In Statistics: In Honour Of Professor John Nelder, Frs written by David J Hand and published by World Scientific. This book was released on 2004-07-06 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: John Nelder was one of the most influential statisticians of his generation, having made an impact on many parts of the discipline. This book contains reviews of some of those areas, written by top researchers. It is accessible to non-specialists, and is noteworthy for its breadth of coverage.
Book Synopsis Discrete Choice Methods with Simulation by : Kenneth Train
Download or read book Discrete Choice Methods with Simulation written by Kenneth Train and published by Cambridge University Press. This book was released on 2009-07-06 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the new generation of discrete choice methods, focusing on the many advances that are made possible by simulation. Researchers use these statistical methods to examine the choices that consumers, households, firms, and other agents make. Each of the major models is covered: logit, generalized extreme value, or GEV (including nested and cross-nested logits), probit, and mixed logit, plus a variety of specifications that build on these basics. Simulation-assisted estimation procedures are investigated and compared, including maximum stimulated likelihood, method of simulated moments, and method of simulated scores. Procedures for drawing from densities are described, including variance reduction techniques such as anithetics and Halton draws. Recent advances in Bayesian procedures are explored, including the use of the Metropolis-Hastings algorithm and its variant Gibbs sampling. The second edition adds chapters on endogeneity and expectation-maximization (EM) algorithms. No other book incorporates all these fields, which have arisen in the past 25 years. The procedures are applicable in many fields, including energy, transportation, environmental studies, health, labor, and marketing.
Book Synopsis Combinatorial Methods in Discrete Distributions by : Charalambos A. Charalambides
Download or read book Combinatorial Methods in Discrete Distributions written by Charalambos A. Charalambides and published by John Wiley & Sons. This book was released on 2005-06-24 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unique approach illustrating discrete distribution theory through combinatorial methods This book provides a unique approach by presenting combinatorial methods in tandem with discrete distribution theory. This method, particular to discreteness, allows readers to gain a deeper understanding of theory by using applications to solve problems. The author makes extensive use of the reduction approach to conditional distributions of independent random occupancy numbers, and provides excellent studies of occupancy and sequential occupancy distributions, convolutions of truncated discrete distributions, and compound and mixture distributions. Combinatorial Methods in Discrete Distributions begins with a brief presentation of set theory followed by basic counting principles. Fundamental principles of combinatorics, finite differences, and discrete probability are included to give readers the necessary foundation to the topics presented in the text. A thorough examination of the field is provided and features: Stirling numbers and generalized factorial coefficients Occupancy and sequential occupancy distributions n-fold convolutions of truncated distributions Compound and mixture distributions Thoroughly worked examples aid readers in understanding complex theory and discovering how theory can be applied to solve practical problems. An appendix with hints and answers to the exercises helps readers work through the more complex sections. Reference notes are provided at the end of each chapter, and an extensive bibliography offers readers a resource for additional information on specialized topics.
Book Synopsis Global Methods for Combinatorial Isoperimetric Problems by : L. H. Harper
Download or read book Global Methods for Combinatorial Isoperimetric Problems written by L. H. Harper and published by Cambridge University Press. This book was released on 2004-02-09 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Certain constrained combinatorial optimization problems have a natural analogue in the continuous setting of the classical isoperimetric problem. The study of so called combinatorial isoperimetric problems exploits similarities between these two, seemingly disparate, settings. This text focuses on global methods. This means that morphisms, typically arising from symmetry or direct product decomposition, are employed to transform new problems into more restricted and easily solvable settings whilst preserving essential structure. This book is based on Professor Harper's many years' experience in teaching this subject and is ideal for graduate students entering the field. The author has increased the utility of the text for teaching by including worked examples, exercises and material about applications to computer science. Applied systematically, the global point of view can lead to surprising insights and results, and established researchers will find this to be a valuable reference work on an innovative method for problem solving.
