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Optimal algorithms for the $$\alpha$$-neighbor $$p$$-center problem. (English) Zbl 1292.90159
Summary: Assigning multiple service facilities to demand points is important when demand points are required to withstand service facility failures. Such failures may result from a multitude of causes, ranging from technical difficulties to natural disasters. The $$\alpha$$-neighbor $$p$$-center problem deals with locating $$p$$ service facilities. Each demand point is assigned to its nearest $$\alpha$$ service facilities, thus it is able to withstand up to $$\alpha-1$$ service facility failures. The objective is to minimize the maximum distance between a demand point and its $$\alpha$$th nearest service facility. We present two optimal algorithms for both the continuous and discrete $$\alpha$$-neighbor $$p$$-center problem. We present experimental results comparing the performance of the two optimal algorithms for $$\alpha=2$$. We also present experimental results showing the performance of the relaxation algorithm for $$\alpha=1, 2, 3$$.

##### MSC:
 90B80 Discrete location and assignment 90C60 Abstract computational complexity for mathematical programming problems