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On the overlap area of a disk and a piecewise circular domain. (English) Zbl 1458.90422
Summary: We provide an approach to solve the problem of locating a disk so that its overlap area with a piecewise circular domain is near-optimal when considering partial converage. To this purpose, we introduce the concept of overlap area map. Both, overlap area maps and near-optimal locations, provide useful tools for solving problems related to the placement, for example, of emergency warning sirens, cellular towers or radio receiving stations, that are commonly encountered in the location science field. We present parallel algorithms on graphics processing units (GPUs) for computing an overlap area map and obtaining a set of near-optimal locations from the overlap area map. These algorithms have as a key element the overlap area computation process to which we pay special attention. In addition, we describe a way of visualizing the obtained solutions. Integration of computation and visualization facilitates decision makers, with an iterative what-if-analysis process, to gain more information in order to facilitate the selection of an appropriate location. Finally, we also provide and discuss experimental results showing the efficiency and scalability of our approach.
MSC:
90B80 Discrete location and assignment
90B50 Management decision making, including multiple objectives
90-08 Computational methods for problems pertaining to operations research and mathematical programming
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