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A polynomial time algorithm for a hemispherical minimax location problem
Affiliation:1. Yale School of Medicine, New Haven, CT, USA;2. Radboudumc, Nijmegen, The Netherlands;3. National Institutes of Health, Bethesda, MD, USA;4. René Descartes University, Paris, France;5. University of Toronto, Sunnybrook Health Sciences Centre, Toronto, Canada;6. Johns Hopkins University, Baltimore, MD, USA;7. University of California, Los Angeles, CA, USA;8. University of Pennsylvania, Philadelphia, USA;9. AdMeTech Foundation, Boston, MA, USA;10. Harvard University, Boston, MA, USA;11. University Hospital of Bern, Bern, Switzerland;12. University of Cincinnati, Cincinnati, OH, USA;1. Department of Polymer & Materials Chemistry, Faculty of Chemistry and Petroleum Science, Shahid Beheshti University, GC, 1983969411 Tehran, Iran;2. Department of Petroleum Engineering, Kazan Federal University, Kremlevskaya str. 18, 420008 Kazan, Russian Federation;3. Faculty of Chemical, Petroleum and Gas Engineering, Semnan University, Semnan, Iran;4. Department of Chemistry, K. N. Toosi University of Technology, Tehran, Iran;1. Department of Mathematics, College of Science, University of Zakho, Duhok-42001, Iraq;2. Department of Mathematics, Radfan University College, University of Lahej, Lahej, Yemen;3. Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia;4. Faculty of Exact and Natural Sciences, School of Physical Sciences and Mathematics, Pontifical Catholic University of Ecuador, Av. 12 de octubre 1076 y Roca, Apartado Postal 17-01-2184, Sede Quito, Ecuador;1. Ball State University, United States;2. Utah State University, United States;1. School of Statistics, Dongbei University of Finance and Economics, Dalian, 116025, China;2. College of Letters and Science, University of California-Los Angeles, Los Angeles, CA, 90024, USA
Abstract:A polynomial time algorithm to obtain an exact solution for the equiweighted minimax location problem when the demand points are spread over a hemisphere is presented. It is shown that the solution of the minimax problem when the norm under consideration is geodesic is equivalent to solving a maximization problem using the Euclidean norm.
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