Locating a Central Hunter on the Plane
Locating a Central Hunter on the Plane
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DOI：
10.1007/s10957-007-9293-y
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发表时间：
2008-02
影响因子：
1.9
通讯作者：
M. Cera;J. A. Mesa;F. Ortega;F. Plastria
中科院分区：
文献类型：
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作者：
M. Cera;J. A. Mesa;F. Ortega;F. Plastria
移动点的保护、监视或其他类型的覆盖服务需要与固定点使用的传统欧几里得、矩形或其他标准不同的、不对称的距离测量。在本文中，目的地是以固定速度和方向移动的移动点（猎物），设施（猎人）可以使用两种可能的策略之一捕获它们：要么是聪明的，预测猎物的运动，以最大限度地减少捕获它所需的时间，要么是愚蠢的，遵循追踪曲线，随时向猎物的方向移动。无论哪种情况，都会寻找猎人在飞机上的位置，以尽量减少捕获任何猎物的最大时间。开发了一种有效的求解算法，该算法使用该问题的两个版本都具有的特定几何形状。在猎物运动不可预测的情况下，提出了最坏情况类型的解决方案，该解决方案简化为众所周知的加权欧几里德极小极大位置问题。
Protection, surveillance or other types of coverage services of mobile points call for different, asymmetric distance measures than the traditional Euclidean, rectangular or other norms used for fixed points. In this paper, the destinations are mobile points (prey) moving at fixed speeds and directions and the facility (hunter) can capture them using one of two possible strategies: either it is smart, predicting the prey’s movement in order to minimize the time needed to capture it, or it is dumb, following a pursuit curve, by moving at any moment in the direction of the prey. In either case, the hunter location in a plane is sought in order to minimize the maximum time of capture of any prey. An efficient solution algorithm is developed that uses the particular geometry that both versions of this problem possess. In the case of unpredictable movement of prey, a worst-case type solution is proposed, which reduces to the well-known weighted Euclidean minimax location problem.