An algorithm and a core set result for the weighted euclidean one-center problem
| dc.citation.epage | 629 | en_US |
| dc.citation.issueNumber | 4 | en_US |
| dc.citation.spage | 614 | en_US |
| dc.citation.volumeNumber | 21 | en_US |
| 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.department | Department of Industrial Engineering | en_US |
| 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.description.provenance | Made available in DSpace on 2016-02-08T10:02:52Z (GMT). No. of bitstreams: 1 bilkent-research-paper.pdf: 70227 bytes, checksum: 26e812c6f5156f83f0e77b261a471b5a (MD5) Previous issue date: 2009 | en |
| dc.identifier.doi | 10.1287/ijoc.1080.0315 | en_US |
| dc.identifier.eissn | 1526-5528 | |
| dc.identifier.issn | 1091-9856 | |
| dc.identifier.uri | http://hdl.handle.net/11693/22646 | |
| dc.language.iso | English | en_US |
| dc.publisher | Institute for Operations Research and the Management Sciences (I N F O R M S) | en_US |
| dc.relation.isversionof | http://dx.doi.org/10.1287/ijoc.1080.0315 | en_US |
| dc.source.title | INFORMS Journal on Computing | 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 |
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