Algorithmic Aspects Of Combinatorics
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Algorithmic Aspects Of Combinatories
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Author : Brian Roger Alspach
language : en
Publisher:
Release Date : 1978
Algorithmic Aspects Of Combinatories written by Brian Roger Alspach and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Algorithms categories.
Algorithmic Aspects Of Combinatorics
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Author : B. Alspach
language : en
Publisher: Elsevier
Release Date : 1978-01-01
Algorithmic Aspects Of Combinatorics written by B. Alspach and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978-01-01 with Mathematics categories.
Algorithmic Aspects of Combinatorics
Geometric Algorithms And Combinatorial Optimization
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Author : Martin Grötschel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometric Algorithms And Combinatorial Optimization written by Martin Grötschel 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.
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.
Combinatorial Algorithms
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Author : Donald L. Kreher
language : en
Publisher: CRC Press
Release Date : 1998-12-18
Combinatorial Algorithms written by Donald L. Kreher and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-12-18 with Mathematics categories.
This textbook thoroughly outlines combinatorial algorithms for generation, enumeration, and search. Topics include backtracking and heuristic search methods applied to various combinatorial structures, such as: Combinations Permutations Graphs Designs Many classical areas are covered as well as new research topics not included in most existing texts, such as: Group algorithms Graph isomorphism Hill-climbing Heuristic search algorithms This work serves as an exceptional textbook for a modern course in combinatorial algorithms, providing a unified and focused collection of recent topics of interest in the area. The authors, synthesizing material that can only be found scattered through many different sources, introduce the most important combinatorial algorithmic techniques - thus creating an accessible, comprehensive text that students of mathematics, electrical engineering, and computer science can understand without needing a prior course on combinatorics.
Algorithms In Combinatorial Geometry
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Author : Herbert Edelsbrunner
language : en
Publisher: Springer Science & Business Media
Release Date : 1987-07-31
Algorithms In Combinatorial Geometry written by Herbert Edelsbrunner 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 1987-07-31 with Computers categories.
Computational geometry as an area of research in its own right emerged in the early seventies of this century. Right from the beginning, it was obvious that strong connections of various kinds exist to questions studied in the considerably older field of combinatorial geometry. For example, the combinatorial structure of a geometric problem usually decides which algorithmic method solves the problem most efficiently. Furthermore, the analysis of an algorithm often requires a great deal of combinatorial knowledge. As it turns out, however, the connection between the two research areas commonly referred to as computa tional geometry and combinatorial geometry is not as lop-sided as it appears. Indeed, the interest in computational issues in geometry gives a new and con structive direction to the combinatorial study of geometry. It is the intention of this book to demonstrate that computational and com binatorial investigations in geometry are doomed to profit from each other. To reach this goal, I designed this book to consist of three parts, acorn binatorial part, a computational part, and one that presents applications of the results of the first two parts. The choice of the topics covered in this book was guided by my attempt to describe the most fundamental algorithms in computational geometry that have an interesting combinatorial structure. In this early stage geometric transforms played an important role as they reveal connections between seemingly unrelated problems and thus help to structure the field.
Algorithmic Aspects Of Graph Connectivity
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Author : Hiroshi Nagamochi
language : en
Publisher: Cambridge University Press
Release Date : 2019-05-16
Algorithmic Aspects Of Graph Connectivity written by Hiroshi Nagamochi 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 2019-05-16 with Computers categories.
Algorithmic Aspects of Graph Connectivity is the first comprehensive book on this central notion in graph and network theory, emphasizing its algorithmic aspects. Because of its wide applications in the fields of communication, transportation, and production, graph connectivity has made tremendous algorithmic progress under the influence of the theory of complexity and algorithms in modern computer science. The book contains various definitions of connectivity, including edge-connectivity and vertex-connectivity, and their ramifications, as well as related topics such as flows and cuts. The authors comprehensively discuss new concepts and algorithms that allow for quicker and more efficient computing, such as maximum adjacency ordering of vertices. Covering both basic definitions and advanced topics, this book can be used as a textbook in graduate courses in mathematical sciences, such as discrete mathematics, combinatorics, and operations research, and as a reference book for specialists in discrete mathematics and its applications.
Probabilistic Methods For Algorithmic Discrete Mathematics
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Author : Michel Habib
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-08-19
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 1998-08-19 with Computers categories.
The book gives an accessible account of modern pro- babilistic methods for analyzing combinatorial structures and algorithms. Each topic is approached in a didactic manner but the most recent developments are linked to the basic ma- terial. Extensive lists of references and a detailed index will make this a useful guide for graduate students and researchers. Special features included: - a simple treatment of Talagrand inequalities and their applications - an overview and many carefully worked out examples of the probabilistic analysis of combinatorial algorithms - a discussion of the "exact simulation" algorithm (in the context of Markov Chain Monte Carlo Methods) - a general method for finding asymptotically optimal or near optimal graph colouring, showing how the probabilistic method may be fine-tuned to explit the structure of the underlying graph - a succinct treatment of randomized algorithms and derandomization techniques
Analytic Combinatorics
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Author : Philippe Flajolet
language : en
Publisher: Cambridge University Press
Release Date : 2009-01-15
Analytic Combinatorics written by Philippe Flajolet 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 2009-01-15 with Mathematics categories.
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.
Combinatorial Optimization
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Author : Bernhard H. Korte
language : en
Publisher: Springer Science & Business Media
Release Date : 2006
Combinatorial Optimization written by Bernhard H. Korte 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 2006 with Computers categories.
This comprehensive textbook on combinatorial optimization puts special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. It has arisen as the basis of several courses on combinatorial optimization and more special topics at graduate level. Since the complete book contains enough material for at least four semesters (4 hours a week), one usually selects material in a suitable way. The book contains complete but concise proofs, also for many deep results, some of which did not appear in a book before. Many very recent topics are covered as well, and many references are provided. Thus this book represents the state of the art of combinatorial optimization. This third edition contains a new chapter on facility location problems, an area which has been extremely active in the past few years. Furthermore there are several new sections and further material on various topics. New exercises and updates in the bibliography were added. From the reviews of the 2nd edition: "This book on combinatorial optimization is a beautiful example of the ideal textbook." Operations Resarch Letters 33 (2005), p.216-217 "The second edition (with corrections and many updates) of this very recommendable book documents the relevant knowledge on combinatorial optimization and records those problems and algorithms that define this discipline today. To read this is very stimulating for all the researchers, practitioners, and students interested in combinatorial optimization." OR News 19 (2003), p.42
Aspects Of Combinatorics
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Author : Victor Bryant
language : en
Publisher: Cambridge University Press
Release Date : 1993-01-14
Aspects Of Combinatorics written by Victor Bryant 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 1993-01-14 with Mathematics categories.
Combinatorics is a broad and important area of mathematics, and this textbook provides the beginner with the ideal introduction to many of the different aspects of the subject.