On the parameterized complexity of the Maximum Exposure Problem

We investigate the parameterized complexity of the Maximum Exposure Problem (MEP). Given a range space (R,P) where R is the set of ranges containing a set P of points and an integer k, MEP asks for k ranges, which on removal results in the maximum number of exposed points. A point p is said to be exposed when p is not contained in any of the ranges in R. The problem is known to be NP-hard. In this paper, we give fixed-parameter tractable results of MEP with respect to different parameterizations. •Maximum Exposure Problem (MEP) is not studied till date in the realm of parameterized complexity.•MEP is proved to be W[1]-hard with respect to the solution size, using parameterized reductions.•MEP is proved to be Fixed Parameter Tractable (FPT) for a multiparameterization.•MEP is proved to be Fixed Parameter Tractable (FPT) with respect to the number of cells that contain points.