This book aims to present recent developments and new trends in Combinatorial Optimization. The topics will include, among others, complexity analysis, exact and heuristic methods, cutting-plane techniques, approximations algorithms, computational complexity and network design algorithms.
Combinatorial Optimization is an active research area that has applications in many domains such as communications, network design, VLSI, scheduling, production and computational biology. In recent years, new results and major advances have been seen in many areas including computational complexity, approximation algorithms, cutting-plane-based methods and submodularity function minimization. More efficient and powerful methods have been developed for approaching real-world problems, and new concepts and theoretical results have been introduced. This book presents a collection of chapters surveying some of these advances.
1. Partition Inequalities: Separation, Extensions, and Network Design, Mourad Baïou, Francisco Barahona and A. Ridha Mahjoub.
2. Stable Sets in Claw-Free Graphs: A Journey Through Algorithms and Polytopes, Yuri Faenza, Gianpaolo Oriolo, Gautier Stauffer and Paolo Ventura.
3. Algorithms for Submodular Totally Dual Integral Problems, S. Thomas McCormick.
4. Finding Descriptions of Polytopes via Extended Formulations and Liftings, Volker Kaibel and Andreas Loos.
5. Relax-and-Cut as a Preprocessor and Warm Starter to Branch-and-Cut, Abilio Lucena, Nelson Maculan and Alexandre Salles da Cunha.
6. Weighted Transversals and Blockers for Some Optimization Problems in Graphs, Cédric Bentz, Marie-Christine Costa, Dominique De Werra, Christophe Picouleau and Bernard Ries.
7. On a Time-Dependent Formulation and an Updated Classification of ATSP Formulations, Maria Teresa Godinho, Luis Gouveia and Pierre Pesneau.
8. Cuts Over Extended Formulations by Flow Discretization, Eduardo Uchoa.
9. Model Equivalents and Cutting-Plane Decomposition Methods for Dominance-Constrained Two-stage Stochastic Programs, Dimitri Drapkin, Oliver Klaar and Rüdiger Schultz.
10. Combinatorial Optimization Problems Arising from Interactive Congestion Situations, Laurent Gourvès and Stefano Moretti.
11. Combinatorial Optimization Methods to Determine the Rank of a Matrix over a Communicative Ring, with Engineering Applications, András Recski.
12. Robust Routing in Communication Networks, Walid Ben-Ameur, Adam Ouorou and Mateusz Zotkiewicz.
13. Single Machine Scheduling with a Common Due Date: Total Weighted Tardiness Problems, Imed Kacem, Hans Kellerer and Vitaly Strusevich.
14. Convergent Tabu Search for Optimal Partitioning, Fred Glover and Saïd Hanafi.
15. An Introduction to Exponential Time Exact Algorithms for Solving NP-hard Problems, Nicolas Bourgeois, Bruno Escoffier and Vangelis Th. Paschos.
16. Moderately Exponential Approximation, Nicolas Bourgeois, Bruno Escoffier, Vangelis Th. Paschos and Emeric Tourniaire.
17. Progress in Semidefinite Optimization Techniques for Satisfiability, Miguel F. Anjos.
18. Disjunctive Cuts for Mixed Integer Nonlinear Programming Problems, Pierre Bonami, Jeff Linderoth and Andrea Lodi.
19. Using Extended MIP Formulations for a Production/Sequencing and a Production/Distribution Problem, Laurence A. Wolsey.
20. The Two-Phase Method for Multiobjective Combinatorial Optimization Problems, Anthony Przybylski, Xavier Gandibleux and Matthias Ehrgott.
A. Ridha Mahjoub is Professor of Operations Research and Combinatorial Optimization at the Paris-Dauphine University, France and member of the LAMSADE laboratory CNRS. His research areas include the theory and applications of polyhedral approaches for solving large NP-hard combinatorial optimization problems, linear and integer programming, network design as well as complexity and graph theory. His publications have appeared in numerous leading journals and he serves as Associate Editor for the journal RAIRO-Operations Research.