1.5D terrain guarding problem parameterized by guard range

The 1.5D terrain guarding problem examines a 1.5D terrain as an x-monotone polygonal chain in a plane to find the minimum guarding set for a given input terrain. This problem is NP-complete. In real world applications, guard power is limited and can only cover things within a range. Considering this limitation, the present study introduces the “terrain guard range” as a new geometric parameter by discretizing the definition of range, then presents a fixed-parameter algorithm to demonstrate that the 1.5D terrain guarding problem is fixed-parameter tractable with respect to the introduced parameter.