Abstract
In this paper we discuss a collection of geometric location problems in the plane and their associated time complexity. These problems can be formulated as optimization problems. However, geometric properties are exploited to obtain efficient solutions. Among the problems considered are minimum enclosing circle, largest empty circle, fixed circle placement, and their variations. Most of the algorithms mentioned are asymptotically optimal to within a constant factor under the algebraic computation tree model. Finally, a geometric competitive location problem is discussed and some open problems suggested.
Supported in part by the National Science Foundation under Grants ECS8340031 and DCS8420814.
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Lee, D.T. (1986). Geometric location problems and their complexity. In: Gruska, J., Rovan, B., Wiedermann, J. (eds) Mathematical Foundations of Computer Science 1986. MFCS 1986. Lecture Notes in Computer Science, vol 233. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0016240
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DOI: https://doi.org/10.1007/BFb0016240
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