This book consists of six articles that came out of the following eight lecture series given at the NATO Advanced Study Institute (ASI) “Combinatorial Optimization: Methods and Applications” held at Université de Montréal on June 19 – 30, 2006:

Gérard Cornuéjols

(Carnegie Mellon University, USA)

Mixed integer programming

Sanjeeb Dash

(IBM Thomas J. Watson Research Center, USA)

Mixed integer rounding cuts and cyclic group polyhedra

Yury Kochetov

(Sobolev Institute of Mathematics, Russia)

Facility location problems. Discrete models and local search methods

Bernhard Korte; substituted by Stephan Held after the first lecture

(Forschungsinstitut für Diskrete Mathematik, Germany)

Making chips faster

Gleb Koshevoy

(Russian Academy of Sciences, Russia)

Discrete convexity and its applications in combinatorics

Shmuel Onn

(Technion - Israel Institute of Technology, Israel)

Convex discrete optimization

Dieter Rautenbach

(Institut für Optimierung und Operations Research Universität Ulm, Ulm, Germany)

Optimization and timing in VLSI design

Jens Vygen

(Forschungsinstitut für Diskrete Mathematik, Germany)

Combinatorial optimization in VLSI placement and routing

The six articles are ordered alphabetically by the last name of their first author. The article by Nannicini et al. has been written in 2010 as a follow-up to the lectures given by Cornuéjols at the ASI. The article by Onn is a reprint of his monograph published by Springer in Encyclopedia of Optimization 2009, which follows the outline of his lectures given at the ASI. The remaining four articles also follow the lectures given at the ASI, but they have been updated in 2010.