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978-3-8439-0745-3, Reihe Mathematik
Matthias W. Altenhöfer
Combinatorial Structures in Steel Production Optimization and Social Network Modeling
135 Seiten, Dissertation Technische Universität Kaiserslautern (2012), Softcover, A5
A well known tool for modeling and solving a variety of combinatorial problems are networks. The thesis at hand consists of two parts, treating the subject of networks from different angles.
The Hot Steel Rolling problem treated in the first part asks to find an efficient way to group items - in this case steel slabs or coils - into so called programs that are feasible for production. The combinatorial formulation yields a very large integer program, which can be tackled by a column generation technique. The first chapters of this thesis investigate ways of formulating the underlying networks and discuss exact and approximate methods.
The second part of this thesis addresses models of communication networks such as the web graph. Among the properties of such networks is that nodes with similar information or interest tend to be closely connected. In this work, we introduce means of strengthening the potency of the dot product model.