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Double bound method for solving the \(p\)-center location problem. (English) Zbl 1348.90384
Summary: We give a review of existing methods for solving the absolute and vertex restricted \(p\)-center problems on networks and propose a new integer programming formulation, a tightened version of this formulation and a new method based on successive restrictions of the new formulation. A specialization of the new method with two-element restrictions obtains the optimal \(p\)-center solution by solving a series of simple structured integer programs in recognition form. This specialization is called the double bound method. A relaxation of the proposed formulation gives the tightest known lower bound in the literature (obtained earlier by S. Elloumi et al. [INFORMS J. Comput. 16, No. 1, 84–94 (2004; Zbl 1239.90103)]). A polynomial time algorithm is presented to compute this bound. New lower and upper bounds are proposed. Problems from the OR-Library and TSPLIB are solved by the proposed algorithms with up to 3038 nodes. Previous computational results were restricted to networks with at most 1817 nodes.

90B80 Discrete location and assignment
05C12 Distance in graphs
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