Drones and other small unmanned aerial vehicles are starting to get permission to fly within city limits. While video cameras are easily available in most cities, their purpose is to guard the streets at ground level. Guarding the aerial space of a city with video cameras is a problem that so far has been largely ignored. In this paper, we present bounds on the number of cameras needed to guard the city's aerial space (roofs, walls, and ground) using cameras with 180-degree range of vision (the region in front of the guard), which is common for most commercial cameras. We assume all buildings are vertical and have a rectangular base. Each camera is placed at a top corner of a building. We considered the following two versions: (i) buildings have an axis-aligned ground base and, (ii) buildings have an arbitrary orientation. We give necessary and sufficient results for (i), necessary results for (ii), and conjecture sufficiency results for (ii). Specifically, for (i) we prove a sufficiency bound of 2k + k/4 +4 on the number of vertex guards, while for (ii) we show that 3k + 1 vertex guards are sometimes necessary, where k is the total number of buildings in the city.

中文翻译：

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有限视野的城市守卫

无人机和其他小型无人驾驶飞行器开始获得在城市范围内飞行的许可。虽然大多数城市都可以轻松使用摄像机，但它们的目的是保护地面街道。用摄像机保护城市的空中空间是一个迄今为止在很大程度上被忽视的问题。在本文中，我们提出了使用具有 180 度视野（警卫前方的区域）的摄像机来保护城市空中空间（屋顶、墙壁和地面）所需的摄像机数量的界限，这对于大多数商用相机。我们假设所有建筑物都是垂直的，并有一个矩形底座。每个摄像机都放置在建筑物的顶角。我们考虑了以下两个版本：(i) 建筑物具有轴对齐的地面基础，(ii) 建筑物具有任意方向。我们给出了（i）的充分必要结果，（ii）的必要结果，以及（ii）的猜想充分性结果。具体来说，对于 (i)，我们证明了顶点保护数量的 2k + k/4 +4 的充分界限，而对于 (ii)，我们表明有时需要 3k + 1 个顶点保护，其中 k 是顶点保护的总数城市中的建筑物。