## Large-scale hierarchical networks: How to compute an optimal architecture?

Please always quote using this URN: urn:nbn:de:0297-zib-7799
• In this article, we present a mathematical model and an algorithm to support one of the central strategic planning decisions of network operators: How to organize a large number of locations into a hierarchical network? We propose a solution approach that is based on mixed-integer programming and Lagrangian relaxation techniques. As major advantage, our approach provides not only solutions but also worst-case quality guarantees. Real-world scenarios with more than 750 locations have been solved within 30 minutes to less than 1\% off optimality.

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Author: Andreas Bley, Thorsten Koch, Roland Wessäly ZIB-Report Hierarchical Networks ; Lagrangian Relaxation; Mixed-Integer Programming 68-XX COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area) / 68Mxx Computer system organization / 68M10 Network design and communication [See also 68R10, 90B18] 90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C11 Mixed integer programming 2004/01/19 ZIB-Report (04-04) App. in Networks 2004: 11th International Telecomunications Network Strategy and Planning Symposium 2004, Vienna, Austria, pp. 429-434, H. Kaindl (ed.), VDE Verlag, ISBN 3-8007-2840-0

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