Concepts of Combinatorial Optimization (eBook)

Vangelis T. Paschos is Professor of Computer Science at the University of Paris-Dauphine and Chairman of the LAMSADE (Laboratory for the Modeling and the Analysis of Decision Aiding Systems). His research interests include complexity theory, the theory of the polynomial approximation of NP-hard problems, probabilistic combinatorial optimization and on-line computation. He is the author of more than a 100 research papers and is a member of the editorial board of several international scientific journals.

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