Jon Lee focuses on key mathematical ideas leading to useful models and algorithms, rather than on data structures and implementation details, in this introductory graduate-level text for students of operations research, mathematics, and computer science. The viewpoint is polyhedral, and Lee also uses matroids as a unifying idea. Topics include linear and integer programming, polytopes, matroids and matroid optimization, shortest paths, and network flows. Problems and exercises are included throughout as well as references for further study.
A First Course in Combinatorial Optimization
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Editorial Reviews
Review
"Lee strikes a perfect balance between the specific and the general, between the concrete and the abstract."
CHOICE
“The author, with his light but rigorous mathematical writing style, takes delight in revealing the stars of combinatorial optimization. This is an excellent teaching book; I recommend it highly.”
International Statistical Institute
"The book is attractively laid out on the page and there are lots of good diagrams. Algorithms are separated visually in special boxes and are easy to track down. There are plenty of problems (short proofs) and exercises (calculations) and they are well integrated with the text."
MAA Reviews, Bill Satzer
"Jon Lee's A First Course in Combinatorial Optimization is a brilliant introduction to the topic." - Ryan B. Hayward, University of Alberta
CHOICE
“The author, with his light but rigorous mathematical writing style, takes delight in revealing the stars of combinatorial optimization. This is an excellent teaching book; I recommend it highly.”
International Statistical Institute
"The book is attractively laid out on the page and there are lots of good diagrams. Algorithms are separated visually in special boxes and are easy to track down. There are plenty of problems (short proofs) and exercises (calculations) and they are well integrated with the text."
MAA Reviews, Bill Satzer
"Jon Lee's A First Course in Combinatorial Optimization is a brilliant introduction to the topic." - Ryan B. Hayward, University of Alberta
Book Description
"A First Course in Combinatorial Optimization" is a self-contained text for a one-semester introductory graduate-level course for students of operations research, mathematics, and computer science. The author focuses on the key mathematical ideas that lead to useful models and algorithms rather than on data structures and implementation details. The viewpoint is polyhedral, and the author also uses matroids as a unifying idea.Topics include linear and integer programming, polytopes, matroids and matroid optimization, shortest paths, and network flows. Problems and exercises are included throughout as well as references for further study.
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Inside This Book
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First Sentence:
In this chapter, we review many of the main ideas and results concerning polytopes and linear programming. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
knapsack program, vertex requirements, augmenting path with respect, minimizing submodular functions, alternating forest, vertex packing, graphic matroid, primal simplex method, dual simplex method, simplex table, cover inequality, total unimodularity, common ground set, vertex sequence, optimal objective value, maximal independent subset, primal feasible, rank inequalities, interior vertices, dual feasible, group relaxation, augmenting paths, matroid theory, perfect matching, independence system Key Phrases - Capitalized Phrases (CAPs): (learn more)
Maximum-Flow Algorithm, Weak Duality Theorem, Cardinality Matroid-Intersection Algorithm, Christofides's Heuristic, Edmonds's Maximum-Cardinality Matching Algorithm, Proof Let, Augmenting-Path Procedure, Farkas Lemma, Hall's Theorem, Shrinking Lemma, Strong Duality Theorem, Fourier-Motzkin Elimination, Generic Cutting-Plane Method, Min-Cut Theorem, Swapping Algorithm, Weyl's Theorem, Proof Suppose New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
In this chapter, we review many of the main ideas and results concerning polytopes and linear programming. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
knapsack program, vertex requirements, augmenting path with respect, minimizing submodular functions, alternating forest, vertex packing, graphic matroid, primal simplex method, dual simplex method, simplex table, cover inequality, total unimodularity, common ground set, vertex sequence, optimal objective value, maximal independent subset, primal feasible, rank inequalities, interior vertices, dual feasible, group relaxation, augmenting paths, matroid theory, perfect matching, independence system Key Phrases - Capitalized Phrases (CAPs): (learn more)
Maximum-Flow Algorithm, Weak Duality Theorem, Cardinality Matroid-Intersection Algorithm, Christofides's Heuristic, Edmonds's Maximum-Cardinality Matching Algorithm, Proof Let, Augmenting-Path Procedure, Farkas Lemma, Hall's Theorem, Shrinking Lemma, Strong Duality Theorem, Fourier-Motzkin Elimination, Generic Cutting-Plane Method, Min-Cut Theorem, Swapping Algorithm, Weyl's Theorem, Proof Suppose New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 31
books:
See all 31 books this book cites
4
books
cite this book:
- Combinatorial Optimization (3 volume, A,B, & C) by Alexander Schrijver in Back Matter (1), and Back Matter (2)
- A Tale Of Two Cities by Charles Dickens on page 202
- Oriented Matroids (Encyclopedia of Mathematics and its Applications) by Anders Björner in Back Matter
- Combinatorial Optimization: Annotated Bibliographies by M. O'Heigeartaigh in Back Matter
- Perturbation Methods (Cambridge Texts in Applied Mathematics) by E. J. Hinch in Front Matter
See all 31 books this book cites
- An Introduction to Parallel and Vector Scientific Computing (Cambridge Texts in Applied Mathematics) by Ronald W. Shonkwiler in Front Matter
- Practical Applied Mathematics: Modelling, Analysis, Approximation (Cambridge Texts in Applied Mathematics) by Sam Howison in Front Matter
- Efficient Approximation and Online Algorithms: Recent Progress on Classical Combinatorial Optimization Problems and New Applications (Lecture Notes in ... Computer Science and General Issues) by Evripidis Bampis on page 72
- Composite Systems Decisions (Decision Engineering) by Mark Sh. Levin in Back Matter
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