Maximizing area-range sum for spatial shapes (MAxRS 3 )
Muhammed Mas-ud Hussain, Goce Trajcevski · 2018
We investigate a novel variant of the well-known MaxRS (Maximizing Range Sum) problem - namely, the MAxRS3 (Maximizing Area-Range Sum for Spatial Shapes). The MaxRS problem amounts to detecting a location where a fixed-size rectangle R should be placed, so that it covers a maximum number of points - or sum of weights, if the points are weighted - from a given input set of 2D points. While variants have tackled the settings in which the input set to MaxRS problem consists of polygons instead of points - the solution is still based on (weighted) count. We postulate that in many practical applications it is of interest to determine where to place the input rectangle so that the total area-coverage in its interior is maximized. In this paper, we formalize the MAxRS3 problem and propose (to our knowledge) the first solution to this new problem.