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.
Inhaltsverzeichnis
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
Über den Autor
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.
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