## Integer and combinatorial optimizationRave 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. |

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### Contents

Graphs and Networks | 50 |

Strong Valid Inequalities and Facets for Structured Integer Programs | 259 |

Valid Inequalities for the 01 Knapsack Polytope | 265 |

Copyright | |

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0-1 integer programming 2-matching augmenting path branch-and-bound C-G inequality clique column combinatorial optimization consider constraints contains conv(S convex hull Corollary define digraph dipath dual feasible dual solution duality edges Example extreme points facet feasibility problem feasible solution finite formulation given graph G greedy algorithm greedy heuristic Hence incidence matrix integer programming Iteration knapsack problem linear programming relaxation matching matroid max{cx maximal maximum-weight path minimal minimum-weight mixed-integer node packing nondecreasing nonnegative objective function obtain optimal solution optimization problems otherwise perfect graphs polyhedra polyhedron polymatroid polynomial polynomial-time algorithm polytope programming problem Proof Proposition pseudonode satisfies Section shown in Figure simplex algorithm solve subgraph subset subtour superadditive Suppose Theorem traveling salesman problem upper bound valid inequality variables vector weight yields