覆盖分解与平面传感器覆盖问题
Decomposing Coverings and the Planar Sensor Cover Problem
摘要：
我们表明，$k$折叠覆盖使用平移的任意凸多边形可以分解成$Ω(k)$覆盖（使用一个有效的算法）。我们推广这一结果，以获得一个常数因子近似的传感器覆盖问题的传感器的范围是一个给定的凸多边形的平移。在这种推广的关键因素是一个常数因子近似算法的一维版本的传感器覆盖问题，称为限制带覆盖（RSC）的问题，其中传感器的间隔可能不同的长度。我们的RSC算法改进了以前的$O(\log \log \log n)$近似。
英文摘要：
We show that a $k$-fold covering using translates of an arbitrary convex polygon can be decomposed into $Ω(k)$ covers (using an efficient algorithm). We generalize this result to obtain a constant factor approximation to the sensor cover problem where the ranges of the sensors are translates of a given convex polygon. The crucial ingredient in this generalization is a constant factor approximation algorithm for a one-dimensional version of the sensor cover problem, called the Restricted Strip Cover (RSC) problem, where sensors are intervals of possibly different lengths. Our algorithm for RSC improves on the previous $O(\log \log \log n)$ approximation.
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