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.
Table of Contents:
Preface xvii Vangelis Th. Paschos
Part I Paradigmatic Problems 1
Chapter 1 Optimal Satisfiability 3
Cristina Bazgan
Chapter 2 Scheduling Problems 33
Philippe Chrétienne and Christophe Picouleau
Chapter 3 Location Problems 61
Aristotelis Giannakos
Chapter 4 MiniMax Algorithms and Games 89
Michel Koskas
Chapter 5 Two-dimensional Bin Packing Problems 107
Andrea Lodi, Silvano Martello, Michele Monaci and Daniele Vigo
Chapter 6 The Maximum Cut Problem 131
Walid Ben-Ameur, Ali Ridha Mahjoub and José Neto
Chapter 7 The Traveling Salesman Problem and its Variations 173
Jérôme Monnot and Sophie Toulouse
Chapter 8 0-1 Knapsack Problems 215
Gerard Plateau and Anass Nagih
Chapter 9 Integer Quadratic Knapsack Problems 243
Dominique Quadri, Eric Soutif and Pierre Tolla
Chapter 10 Graph Coloring Problems 265
Dominique De Werra and Daniel Kobler
Part II New Approaches 311
Chapter 11 Polynomial Approximation 313
Marc Demange and Vangelis Th. Paschos
Chapter 12 Approximation Preserving Reductions 351
Giorgio Ausiello and Vangelis Th. Paschos
Chapter 13 Inapproximability of Combinatorial Optimization Problems 381
Luca Trevisan
Chapter 14 Local Search: Complexity and Approximation 435
Eric Angel, Petros Christopoulos and Vassilis Zissimopoulos
Chapter 15 On-line Algorithms 473
Giorgio Ausiello and Luca Becchetti
Chapter 16 Polynomial Approximation for Multicriteria Combinatorial Optimization Problems 511
Eric Angel, Evripidis Bampis and Laurent Gourves
Chapter 17 An Introduction to Inverse Combinatorial Problems 547
Marc Demange and Jérôme Monnot
Chapter 18 Probabilistic Combinatorial Optimization 587
Cecile Murat and Vangelis Th. Paschos
Chapter 19 Robust Shortest Path Problems 615
Virginie Gabrel and Cécile Murat
Chapter 20 Algorithmic Games 641
Aristotelis Giannakos and Bangelis Paschos
Chapter 21 Combinatorial Optimization with Competing Agents 675
Diodato Ferraioli, Laurent Gourvès, Stefano Moretti, Fanny Pascual and Olivier Spanjaard
General Bibliography 707
List of Authors 767
Index 773
Summary of Other Volumes in the Series 781
About the Author :
Vangelis 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.
