The paper addresses the problem of locating sensors with a circular field of view so that a given line segment is under full surveillance, which is termed as the Disc  Problems of locating facilities to cover sets of points on networks and planes have been widely studied. This paper focuses on a new covering problem that is motivated by an application where a line segment is to be kept under surveillance using different types of radars. Using reasonable assumptions, some nonlinear covering problems are formulated. Efficient exact algorithms and heuristics are developed and analyzed for "easy" and "hard" cases, respectively.
Agnetis et al. REF address the problem of deploying sensors for full surveillance of a line segment with minimum cost under a defined cost model.
Covering a line segment with variable radius discs
ArXiv
ArXiv
Computer Science Mathematics