Combinatorial Optimization For Undergraduates
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Combinatorial Optimization For Undergraduates
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Author : L. R. Foulds
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Combinatorial Optimization For Undergraduates written by L. R. Foulds 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.
The major purpose of this book is to introduce the main concepts of discrete optimization problems which have a finite number of feasible solutions. Following common practice, we term this topic combinatorial optimization. There are now a number of excellent graduate-level textbooks on combina torial optimization. However, there does not seem to exist an undergraduate text in this area. This book is designed to fill this need. The book is intended for undergraduates in mathematics, engineering, business, or the physical or social sciences. It may also be useful as a reference text for practising engineers and scientists. The writing of this book was inspired through the experience of the author in teaching the material to undergraduate students in operations research, engineering, business, and mathematics at the University of Canterbury, New Zealand. This experience has confirmed the suspicion that it is often wise to adopt the following approach when teaching material of the nature contained in this book. When introducing a new topic, begin with a numerical problem which the students can readily understand; develop a solution technique by using it on this problem; then go on to general problems. This philosophy has been adopted throughout the book. The emphasis is on plausibility and clarity rather than rigor, although rigorous arguments have been used when they contribute to the understanding of the mechanics of an algorithm.
Combinatorial Optimization
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Author : William J. Cook
language : en
Publisher: John Wiley & Sons
Release Date : 2011-09-30
Combinatorial Optimization written by William J. Cook 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 2011-09-30 with Mathematics categories.
A complete, highly accessible introduction to one of today's most exciting areas of applied mathematics One of the youngest, most vital areas of applied mathematics, combinatorial optimization integrates techniques from combinatorics, linear programming, and the theory of algorithms. Because of its success in solving difficult problems in areas from telecommunications to VLSI, from product distribution to airline crew scheduling, the field has seen a ground swell of activity over the past decade. Combinatorial Optimization is an ideal introduction to this mathematical discipline for advanced undergraduates and graduate students of discrete mathematics, computer science, and operations research. Written by a team of recognized experts, the text offers a thorough, highly accessible treatment of both classical concepts and recent results. The topics include: * Network flow problems * Optimal matching * Integrality of polyhedra * Matroids * NP-completeness Featuring logical and consistent exposition, clear explanations of basic and advanced concepts, many real-world examples, and helpful, skill-building exercises, Combinatorial Optimization is certain to become the standard text in the field for many years to come.
Iterative Methods In Combinatorial Optimization
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Author : Lap Chi Lau
language : en
Publisher: Cambridge University Press
Release Date : 2011-04-18
Iterative Methods In Combinatorial Optimization written by Lap Chi Lau 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 2011-04-18 with Computers categories.
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.
Combinatorial Optimization
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Author : Bernhard Korte
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-04
Combinatorial Optimization written by Bernhard 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 2007-11-04 with Mathematics categories.
Now fully updated in a third edition, this is a comprehensive textbook on combinatorial optimization. It puts special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. The book contains complete but concise proofs, also for many deep results, some of which have not appeared in print before. Recent topics are covered as well, and numerous references are provided. 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.
Introduction To Combinatorial Optimization
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Author : Ding-Zhu Du
language : en
Publisher: Springer Nature
Release Date : 2022-09-26
Introduction To Combinatorial Optimization written by Ding-Zhu Du and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-26 with Mathematics categories.
Introductory courses in combinatorial optimization are popular at the upper undergraduate/graduate levels in computer science, industrial engineering, and business management/OR, owed to its wide applications in these fields. There are several published textbooks that treat this course and the authors have used many of them in their own teaching experiences. This present text fills a gap and is organized with a stress on methodology and relevant content, providing a step-by-step approach for the student to become proficient in solving combinatorial optimization problems. Applications and problems are considered via recent technology developments including wireless communication, cloud computing, social networks, and machine learning, to name several, and the reader is led to the frontiers of combinatorial optimization. Each chapter presents common problems, such as minimum spanning tree, shortest path, maximum matching, network flow, set-cover, as well as key algorithms, such as greedy algorithm, dynamic programming, augmenting path, and divide-and-conquer. Historical notes, ample exercises in every chapter, strategically placed graphics, and an extensive bibliography are amongst the gems of this textbook.
Gems Of Combinatorial Optimization And Graph Algorithms
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Author : Andreas S. Schulz
language : en
Publisher: Springer
Release Date : 2016-01-31
Gems Of Combinatorial Optimization And Graph Algorithms written by Andreas S. Schulz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-31 with Business & Economics categories.
Are you looking for new lectures for your course on algorithms, combinatorial optimization, or algorithmic game theory? Maybe you need a convenient source of relevant, current topics for a graduate student or advanced undergraduate student seminar? Or perhaps you just want an enjoyable look at some beautiful mathematical and algorithmic results, ideas, proofs, concepts, and techniques in discrete mathematics and theoretical computer science? Gems of Combinatorial Optimization and Graph Algorithms is a handpicked collection of up-to-date articles, carefully prepared by a select group of international experts, who have contributed some of their most mathematically or algorithmically elegant ideas. Topics include longest tours and Steiner trees in geometric spaces, cartograms, resource buying games, congestion games, selfish routing, revenue equivalence and shortest paths, scheduling, linear structures in graphs, contraction hierarchies, budgeted matching problems, and motifs in networks. This volume is aimed at readers with some familiarity of combinatorial optimization, and appeals to researchers, graduate students, and advanced undergraduate students alike.
Handbook Of Combinatorial Optimization 1
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Author : Dingzhu Du
language : en
Publisher: Springer Science & Business Media
Release Date : 1998
Handbook Of Combinatorial Optimization 1 written by Dingzhu Du 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 with Mathematics categories.
The first of a multi-volume set, which deals with several algorithmic approaches for discrete problems as well as many combinatorial problems. It is addressed to researchers in discrete optimization, and to all scientists who use combinatorial optimization methods to model and solve problems.
Advances In Combinatorial Optimization
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Author : Moustapha Diaby
language : en
Publisher: World Scientific
Release Date : 2016-01-28
Advances In Combinatorial Optimization written by Moustapha Diaby and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-28 with Mathematics categories.
' Combinational optimization (CO) is a topic in applied mathematics, decision science and computer science that consists of finding the best solution from a non-exhaustive search. CO is related to disciplines such as computational complexity theory and algorithm theory, and has important applications in fields such as operations research/management science, artificial intelligence, machine learning, and software engineering. Advances in Combinatorial Optimization presents a generalized framework for formulating hard combinatorial optimization problems (COPs) as polynomial sized linear programs. Though developed based on the ''traveling salesman problem'' (TSP), the framework allows for the formulating of many of the well-known NP-Complete COPs directly (without the need to reduce them to other COPs) as linear programs, and demonstrates the same for three other problems (e.g. the ''vertex coloring problem'' (VCP)). This work also represents a proof of the equality of the complexity classes "P" (polynomial time) and "NP" (nondeterministic polynomial time), and makes a contribution to the theory and application of ''extended formulations'' (EFs). On a whole, Advances in Combinatorial Optimization offers new modeling and solution perspectives which will be useful to professionals, graduate students and researchers who are either involved in routing, scheduling and sequencing decision-making in particular, or in dealing with the theory of computing in general. Contents:IntroductionBasic IP Model Using the TSPBasic LP Model Using the TSPGeneric LP Modeling for COPsNon-Symmetry of the Basic (TSP) ModelNon-Applicability of Extended Formulations TheoryIllustrations for Other NP-Complete COPs Readership: Professionals, graduate students and researchers who are either involved in routing, scheduling and sequencing decision-making in particular, or in dealing with the theory of computing in general. Key Features:The book offers a new proof of the equality of the complexity classes "P" and "NP"Although our approach is developed using the framework of the TSP, it has natural analogs for the other problems in the NP-Complete class thus providing a unified framework for modeling many combinatorial optimization problems (COPs)The book makes a contribution to the theory and application of Extended Formulations (EFs) refining the notion of EFs by separating the case in which that notion is degenerate from the case in which the notion of EF is well defined/meaningful. It separates the case in which the addition of redundant constraints and variables (for the purpose of establishing EF relations) matters from the case in which the addition of redundant constraints and variables does not matterKeywords:Linear Programming;Convex Optimization;Combinatorial Optimization;Traveling Salesman Problem;NP-Complete Problems;P versus NP'
Nonlinear Combinatorial Optimization
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Author : Ding-Zhu Du
language : en
Publisher: Springer
Release Date : 2019-05-31
Nonlinear Combinatorial Optimization written by Ding-Zhu Du and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-31 with Mathematics categories.
Graduate students and researchers in applied mathematics, optimization, engineering, computer science, and management science will find this book a useful reference which provides an introduction to applications and fundamental theories in nonlinear combinatorial optimization. Nonlinear combinatorial optimization is a new research area within combinatorial optimization and includes numerous applications to technological developments, such as wireless communication, cloud computing, data science, and social networks. Theoretical developments including discrete Newton methods, primal-dual methods with convex relaxation, submodular optimization, discrete DC program, along with several applications are discussed and explored in this book through articles by leading experts.
Combinatorial Optimization
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Author : Bernhard H. Korte
language : en
Publisher: Springer
Release Date : 2000-06-05
Combinatorial Optimization written by Bernhard H. Korte and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-06-05 with Computers categories.
This comprehensive textbook on combinatorial optimisation 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 optimisation 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 optimisation.