We consider the problem of deployment of cameras inside a complex indoor setting for surveillance applications. We formulate the problem of the minimum guarding network that places a minimum number of cameras satisfying both visual coverage of the domain and wireless network connectivity. We prove that finding the minimum guarding network in both the geometric setting and discrete setting is NP-hard. We also give a 2-approximation algorithm to the geometric minimum guarding network. Motivated by the connection of this problem with the watchman tour problem and the art gallery problem, we develop two algorithms that generate satisfactory results in a prototype testbed and in our simulations.

Abstract-Homotopic routing asks for a path going around holes according to a given "threading". Paths of different homotopy types can be used to improve load balancing and routing resilience. We propose the first lightweight homotopic routing scheme that generates constant bounded stretch compared to the shortest path of the same homotopy type. Our main insight is that in a sequence of triangles to traverse, a message always routed to the nearest point on the next triangle in the sequence travels at most a constant times the length of any shortest path going through the same sequence of triangles. Our routing scheme operates on two levels enabled by a coarse triangulation. The top level is used to specify and represent the requested homotopy type, while the bottom level executes the local greedy routing on a triangle sequence. After a preprocessing step that triangulates the given region and creates a minimum-size auxiliary structure, routing operates greedily at two different resolutions. We also present simulation analysis in a variety of settings and show that the paths indeed have small stretch in practice, considerably shorter than the bounds guaranteed by the theory.