On a Constrained Optimal Location Algorithm |
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Authors: | Robert Huotari MP Prophet |
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Institution: | (1) Department of Mathematics, Eastern Oregon University, La Grande, Oregon, 97850;(2) Department of Mathematics, University of Northern Iowa, Cedar Falls, Iowa, 50614-0506 |
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Abstract: | In problems of optimal location, one seeks a position or location that optimizes a particular objective function; this objective function typically relates location and distances to a fixed point set. When one's search is restricted to a given set, we refer to this as a constrained optimal location problem. For a finite point set A, there exist numerous finite algorithms to solve optimal location problems. In this paper we demonstrate how an algorithm, solving optimal location problems in inner-product spaces, can be modified to solve certain constrained optimal location problems. We then apply this modification to a particularly simple (and easily implemented) algorithm and investigate the complexity of the result. In particular we improve a known estimate from exponential to polynomial. |
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Keywords: | Chebyshev center symmetric hull constrained approximation |
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