A First Course In Combinatorial Optimization
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| Author | : Jon Lee |
| Publisher | : Cambridge University Press |
| Total Pages | : 232 |
| Release | : 2004-02-09 |
| Genre | : Business & Economics |
| ISBN | : 9780521010122 |
A First Course in Combinatorial Optimization is a text for a one-semester introductory graduate-level course for students of operations research, mathematics, and computer science. It is a self-contained treatment of the subject, requiring only some mathematical maturity. Topics include: linear and integer programming, polytopes, matroids and matroid optimization, shortest paths, and network flows. Central to the exposition is the polyhedral viewpoint, which is the key principle underlying the successful integer-programming approach to combinatorial-optimization problems. Another key unifying topic is matroids. The author does not dwell on data structures and implementation details, preferring to focus on the key mathematical ideas that lead to useful models and algorithms. Problems and exercises are included throughout as well as references for further study.
| Author | : Alexander Schrijver |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 2024 |
| Release | : 2003-02-12 |
| Genre | : Business & Economics |
| ISBN | : 9783540443896 |
From the reviews: "About 30 years ago, when I was a student, the first book on combinatorial optimization came out referred to as "the Lawler" simply. I think that now, with this volume Springer has landed a coup: "The Schrijver". The box is offered for less than 90.- EURO, which to my opinion is one of the best deals after the introduction of this currency." OR-Spectrum
| Author | : Christos H. Papadimitriou |
| Publisher | : Courier Corporation |
| Total Pages | : 530 |
| Release | : 2013-04-26 |
| Genre | : Mathematics |
| ISBN | : 0486320138 |
This graduate-level text considers the Soviet ellipsoid algorithm for linear programming; efficient algorithms for network flow, matching, spanning trees, and matroids; the theory of NP-complete problems; local search heuristics for NP-complete problems, more. 1982 edition.
| Author | : Frank Neumann |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 215 |
| Release | : 2010-11-04 |
| Genre | : Mathematics |
| ISBN | : 3642165443 |
Bioinspired computation methods such as evolutionary algorithms and ant colony optimization are being applied successfully to complex engineering problems and to problems from combinatorial optimization, and with this comes the requirement to more fully understand the computational complexity of these search heuristics. This is the first textbook covering the most important results achieved in this area. The authors study the computational complexity of bioinspired computation and show how runtime behavior can be analyzed in a rigorous way using some of the best-known combinatorial optimization problems -- minimum spanning trees, shortest paths, maximum matching, covering and scheduling problems. A feature of the book is the separate treatment of single- and multiobjective problems, the latter a domain where the development of the underlying theory seems to be lagging practical successes. This book will be very valuable for teaching courses on bioinspired computation and combinatorial optimization. Researchers will also benefit as the presentation of the theory covers the most important developments in the field over the last 10 years. Finally, with a focus on well-studied combinatorial optimization problems rather than toy problems, the book will also be very valuable for practitioners in this field.
| Author | : Bernhard Korte |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 596 |
| Release | : 2006-01-27 |
| Genre | : Mathematics |
| ISBN | : 3540292977 |
This well-written textbook on combinatorial optimization puts special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. The book contains complete (but concise) proofs, as well as many deep results, some of which have not appeared in any previous books.
| Author | : Charles Byrne |
| Publisher | : CRC Press |
| Total Pages | : 313 |
| Release | : 2014-08-11 |
| Genre | : Business & Economics |
| ISBN | : 1482226588 |
Give Your Students the Proper Groundwork for Future Studies in OptimizationA First Course in Optimization is designed for a one-semester course in optimization taken by advanced undergraduate and beginning graduate students in the mathematical sciences and engineering. It teaches students the basics of continuous optimization and helps them better
| Author | : Lap Chi Lau |
| Publisher | : Cambridge University Press |
| Total Pages | : 255 |
| Release | : 2011-04-18 |
| Genre | : Computers |
| ISBN | : 1139499394 |
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.
| Author | : Laurence A. Wolsey |
| Publisher | : John Wiley & Sons |
| Total Pages | : 782 |
| Release | : 2014-08-28 |
| Genre | : Mathematics |
| ISBN | : 1118626869 |
Rave reviews for INTEGER AND COMBINATORIAL OPTIMIZATION "This book provides an excellent introduction and survey of traditional fields of combinatorial optimization . . . It is indeed one of the best and most complete texts on combinatorial optimization . . . available. [And] with more than 700 entries, [it] has quite an exhaustive reference list."-Optima "A unifying approach to optimization problems is to formulate them like linear programming problems, while restricting some or all of the variables to the integers. This book is an encyclopedic resource for such formulations, as well as for understanding the structure of and solving the resulting integer programming problems."-Computing Reviews "[This book] can serve as a basis for various graduate courses on discrete optimization as well as a reference book for researchers and practitioners."-Mathematical Reviews "This comprehensive and wide-ranging book will undoubtedly become a standard reference book for all those in the field of combinatorial optimization."-Bulletin of the London Mathematical Society "This text should be required reading for anybody who intends to do research in this area or even just to keep abreast of developments."-Times Higher Education Supplement, London Also of interest . . . INTEGER PROGRAMMING Laurence A. Wolsey Comprehensive and self-contained, this intermediate-level guide to integer programming provides readers with clear, up-to-date explanations on why some problems are difficult to solve, how techniques can be reformulated to give better results, and how mixed integer programming systems can be used more effectively. 1998 (0-471-28366-5) 260 pp.
| Author | : Dennis Stanton |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 194 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461249686 |
The notes that eventually became this book were written between 1977 and 1985 for the course called Constructive Combinatorics at the University of Minnesota. This is a one-quarter (10 week) course for upper level undergraduate students. The class usually consists of mathematics and computer science majors, with an occasional engineering student. Several graduate students in computer science also attend. At Minnesota, Constructive Combinatorics is the third quarter of a three quarter sequence. The fIrst quarter, Enumerative Combinatorics, is at the level of the texts by Bogart [Bo], Brualdi [Br], Liu [Li] or Tucker [Tu] and is a prerequisite for this course. The second quarter, Graph Theory and Optimization, is not a prerequisite. We assume that the students are familiar with the techniques of enumeration: basic counting principles, generating functions and inclusion/exclusion. This course evolved from a course on combinatorial algorithms. That course contained a mixture of graph algorithms, optimization and listing algorithms. The computer assignments generally consisted of testing algorithms on examples. While we felt that such material was useful and not without mathematical content, we did not think that the course had a coherent mathematical focus. Furthermore, much of it was being taught, or could have been taught, elsewhere. Graph algorithms and optimization, for instance, were inserted into the graph theory course where they naturally belonged. The computer science department already taught some of the material: the simpler algorithms in a discrete mathematics course; effIciency of algorithms in a more advanced course.
| Author | : Michele Conforti |
| Publisher | : Springer |
| Total Pages | : 466 |
| Release | : 2014-11-15 |
| Genre | : Business & Economics |
| ISBN | : 331911008X |
This book is an elegant and rigorous presentation of integer programming, exposing the subject’s mathematical depth and broad applicability. Special attention is given to the theory behind the algorithms used in state-of-the-art solvers. An abundance of concrete examples and exercises of both theoretical and real-world interest explore the wide range of applications and ramifications of the theory. Each chapter is accompanied by an expertly informed guide to the literature and special topics, rounding out the reader’s understanding and serving as a gateway to deeper study. Key topics include: formulations polyhedral theory cutting planes decomposition enumeration semidefinite relaxations Written by renowned experts in integer programming and combinatorial optimization, Integer Programming is destined to become an essential text in the field.
