On guarding real terrains: the terrain guarding and the blocking path problems

Locating a minimum number of guards on a terrain such that every point on the terrain is guarded by at least one of the guards is known as the Terrain Guarding Problem (TGP). In this paper, a realistic example of the terrain guarding problem is studied, involving the surveillance of a rugged geographical terrain by means of thermal cameras. A number of issues related to TGP are addressed with integer-programming models proposed to solve the problem. Also, a sensitivity analysis is carried out in which five fictitious terrains are created to see the effect of the resolution of the terrain, and of terrain characteristics, on coverage optimization and the required number of guards. Finally, a new problem, which is called the Blocking Path Problem (BPP), is introduced. BPP is about guarding a path on the terrain with a minimum number of guards such that the path blocks all possible infiltration routes. A discussion is provided about the relation of BPP to the Network Interdiction Problem (NIP), which has been studied extensively by the operations research community, and to the k-Barrier Coverage Problem, which has been studied under the Sensor Deployment Problem. BPP is solved via an integer-programming formulation based on a network paradigm.