An algorithm and a core set result for the weighted euclidean one-center problem

dc.citation.epage629en_US
dc.citation.issueNumber4en_US
dc.citation.spage614en_US
dc.citation.volumeNumber21en_US
dc.contributor.authorKumar, P.en_US
dc.contributor.authorYıldırım, A. E.en_US
dc.date.accessioned2016-02-08T10:02:52Z
dc.date.available2016-02-08T10:02:52Z
dc.date.issued2009en_US
dc.departmentDepartment of Industrial Engineeringen_US
dc.description.abstractGiven 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.identifier.doi10.1287/ijoc.1080.0315en_US
dc.identifier.eissn1526-5528
dc.identifier.issn1091-9856
dc.identifier.urihttp://hdl.handle.net/11693/22646
dc.language.isoEnglishen_US
dc.publisherInstitute for Operations Research and the Management Sciences (I N F O R M S)en_US
dc.relation.isversionofhttp://dx.doi.org/10.1287/ijoc.1080.0315en_US
dc.source.titleINFORMS Journal on Computingen_US
dc.subjectApproximation algorithmsen_US
dc.subjectCore setsen_US
dc.subjectMinimum enclosing ballsen_US
dc.subjectWeighted euclidean one-center problemen_US
dc.titleAn algorithm and a core set result for the weighted euclidean one-center problemen_US
dc.typeArticleen_US

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