1 research outputs found
City Guarding with Limited Field of View
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