Facets of Combinatorial Optimization

Facets of Combinatorial Optimization

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Martin GrAptschel is one of the most influential mathematicians of our time. He has received numerous honors and holds a number of key positions in the international mathematical community. He celebrated his 65th birthday on September 10, 2013. Martin GrAptschela€™s doctoral descendant tree 1983a€“2012, i.e., the first 30 years, features 39 children, 74 grandchildren, 24 great-grandchildren and 2 great-great-grandchildren, a total of 139 doctoral descendants. This book starts with a personal tribute to Martin GrAptschel by the editors (Part I), a contribution by his very special a€œpredecessora€ Manfred Padberg on a€œFacets and Rank of Integer Polyhedraa€ (Part II), and the doctoral descendant tree 1983a€“2012 (Part III). The core of this book (Part IV) contains 16 contributions, each of which is coauthored by at least one doctoral descendant. The sequence of the articles starts with contributions to the theory of mathematical optimization, including polyhedral combinatorics, extended formulations, mixed-integer convex optimization, super classes of perfect graphs, efficient algorithms for subtree-telecenters, junctions in acyclic graphs and preemptive restricted strip covering, as well as efficient approximation of non-preemptive restricted strip covering. Combinations of new theoretical insights with algorithms and experiments deal with network design problems, combinatorial optimization problems with submodular objective functions and more general mixed-integer nonlinear optimization problems. Applications include VLSI layout design, systems biology, wireless network design, mean-risk optimization and gas network optimization. Computational studies include a semidefinite branch and cut approach for the max k-cut problem, mixed-integer nonlinear optimal control, and mixed-integer linear optimization for scheduling and routing of fly-in safari planes. The two closing articles are devoted to computational advances in general mixed integer linear optimization, the first by scientists working in industry, the second by scientists working in academia. These articles reflect the a€œscientific facetsa€ of Martin GrAptschel who has set standards in theory, computation and applications.On the other hand, this is also an artifact of our bracket definition, since a significant fraction of the models in the [1k, 10k] ... to note that our definition of the subsets of the problem instances depends on the solvers being compared in each table, anbsp;...

Title:Facets of Combinatorial Optimization
Author: Michael Jünger, Gerhard Reinelt
Publisher:Springer Science & Business Media - 2013-07-03

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