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.

Combinatorial optimization is a multidisciplinary scientific arealying in the interface of three major scientific domains:mathematics, theoretical computer science and management. Thethree volumes of the Combinatorial Optimization series aim to covera wide range of topics in this area. These topics also dealwith fundamental notions and approaches as with several classicalapplications of combinatorial optimization.Concepts of Combinatorial Optimization, is divided intothree parts: On the complexity of combinatorial optimization problemspresenting basics about worst-case and randomized complexity; Classical solution methods, presenting the two most-known methodsfor solving hard combinatorial optimization problems, that areBranch-and-Bound and Dynamic Programming; Elements from mathematical programming, presenting fundamentalsfrom mathematical programming based methods that are in the heartof Operations Research since the origins of this field.

Preface xiiiVangelis Th. PaschosPart I Complexity of Combinatioral Optimization Problems1Chapter 1 Basic Concepts in Algorithms and Complexity Theory3Vangelis Th. PaschosChapter 2 Randomized Complexity 21Jérémy BarbayPart II Classic Solution Methods 39Chapter 3 Branch-and-Bound Methods 41Irène Charon and Olivier HudryChapter 4 Dynamic Programming 71Bruno Escoffier and Olivier SpanjaardPart III Elements from Mathematical Programming 101Chapter 5 Mixed Integer Linear Programming Models forCombinatorial Optimization Problems 103Frédérico Della CroceChapter 6 Simplex Algorithms for Linear Programming 135Frédérico Della Croce and Andrea GrossoChapter 7 A Survey of Some Linear Programming Methods 157Pierre TollaChapter 8 Quadratic Optimization in 0-1 Variables 189Alain BillionnetChapter 9 Column Generation in Integar Linear Programming235Irène Loiseau, Alberto Ceselli, Nelson Maculan and MatteoSalaniChapter 10 Polyhedral Approaches 261Ali Ridha MahjoubChapter 11 Constaint Programming 325Claude Le PapeGeneral Bibliography 339List of Authors 363Index 367Summary of Other Volumes in the Series 371