Minimizing the Range for k-Covered Paths on Sensor Networks

Coverage problems are a flourishing topic in optimization, thanks to the recent advances in the field of wireless sensor networks. The main coverage issue centres around critical conditions that require reliable monitoring and prohibit failures. This issue can be addressed by maximal-exposure paths, regarding which this article presents new results. Namely, it shows how to minimize the sensing range of a set of sensors in order to ensure the existence of a k-covered path between two points on a given region. Such a path's coverage depends on k≥2, which is fixed. The three types of regions studied are: a planar graph, the whole plane and a polygonal region.