dc.contributor.author Kumar, P. en_US dc.contributor.author Yıldırım, A. E. en_US dc.date.accessioned 2016-02-08T10:02:52Z dc.date.available 2016-02-08T10:02:52Z dc.date.issued 2009 en_US dc.identifier.issn 1091-9856 dc.identifier.uri http://hdl.handle.net/11693/22646 dc.description.abstract Given a set A of m points in n-dimensional space with corresponding positive weights, the weighted Euclidean one-center problem, which is a generalization of the minimum enclosing ball problem, involves the computation of a point c A n that minimizes the maximum weighted Euclidean distance from c A to each point in A In this paper, given ε > 0, we propose and analyze an algorithm that computes a (1 + ε)-approximate solution to the weighted Euclidean one-center problem. Our algorithm explicitly constructs a small subset X ⊆ A, called an ε-core set of A, for which the optimal solution of the corresponding weighted Euclidean one-center problem is a close approximation to that of A. In addition, we establish that \X\ depends only on ε and on the ratio of the smallest and largest weights, but is independent of the number of points m and the dimension n. This result subsumes and generalizes the previously known core set results for the minimum enclosing ball problem. Our algorithm computes a (1 + ε)-approximate solution to the weighted Euclidean one-center problem for A in O(mn\X\) arithmetic operations. Our computational results indicate that the size of the ε-core set computed by the algorithm is, in general, significantly smaller than the theoretical worst-case estimate, which contributes to the efficiency of the algorithm, especially for large-scale instances. We shed some light on the possible reasons for this discrepancy between the theoretical estimate and the practical performance. en_US dc.language.iso English en_US dc.source.title INFORMS Journal on Computing en_US dc.relation.isversionof http://dx.doi.org/10.1287/ijoc.1080.0315 en_US dc.subject Approximation algorithms en_US dc.subject Core sets en_US dc.subject Minimum enclosing balls en_US dc.subject Weighted euclidean one-center problem en_US dc.title An algorithm and a core set result for the weighted euclidean one-center problem en_US dc.type Article en_US dc.department Department of Industrial Engineering en_US dc.citation.spage 614 en_US dc.citation.epage 629 en_US dc.citation.volumeNumber 21 en_US dc.citation.issueNumber 4 en_US dc.identifier.doi 10.1287/ijoc.1080.0315 en_US dc.publisher Institute for Operations Research and the Management Sciences (I N F O R M S) en_US dc.identifier.eissn 1526-5528
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