Concepts of Combinatorial Optimization

Combinatorial optimization is a multidisciplinary scientific area, lying in the interface of three major scientific domains: mathematics, theoretical computer science and management.  The three volumes of the Combinatorial Optimization series aim to cover a wide range  of topics in this area. These topics also deal with fundamental notions and approaches as with several classical applications of combinatorial optimization. Concepts of Combinatorial Optimization, is divided into three parts: - On the complexity of combinatorial optimization problems, presenting basics about worst-case and randomized complexity; - Classical solution methods, presenting the two most-known methods for solving hard combinatorial optimization problems, that are Branch-and-Bound and Dynamic Programming; - Elements from mathematical programming, presenting fundamentals from mathematical programming based methods that are in the heart of Operations Research since the origins of this field.

Preface xiii Vangelis Th. Paschos Part I Complexity of Combinatioral Optimization Problems 1 Chapter 1 Basic Concepts in Algorithms and Complexity Theory 3 Vangelis Th. Paschos Chapter 2 Randomized Complexity 21 Jérémy Barbay Part II Classic Solution Methods 39 Chapter 3 Branch-and-Bound Methods 41 Irène Charon and Olivier Hudry Chapter 4 Dynamic Programming 71 Bruno Escoffier and Olivier Spanjaard Part III Elements from Mathematical Programming 101 Chapter 5 Mixed Integer Linear Programming Models for Combinatorial Optimization Problems 103 Frédérico Della Croce Chapter 6 Simplex Algorithms for Linear Programming 135 Frédérico Della Croce and Andrea Grosso Chapter 7 A Survey of Some Linear Programming Methods 157 Pierre Tolla Chapter 8 Quadratic Optimization in 0-1 Variables 189 Alain Billionnet Chapter 9 Column Generation in Integar Linear Programming 235 Irène Loiseau, Alberto Ceselli, Nelson Maculan and Matteo Salani Chapter 10 Polyhedral Approaches 261 Ali Ridha Mahjoub Chapter 11 Constaint Programming 325 Claude Le Pape General Bibliography 339 List of Authors 363 Index 367 Summary of Other Volumes in the Series 371