The problem of a maximal weighted area of axis-parallel rectangle that covers polygons

Abstract

The paper presents the problem of finding the optimal location of the rectangle with the maximum weighted area. The dimensions of the rectangle are set, the sides of the rectangle are parallel to the axes. On the plane, there are non-self-intersecting polygons of arbitrary shape with a given density. The weighted area of a rectangle is calculated as a sum of the area of the parts of polygons covered by the rectangle multiplied by their densities. The algorithm for solving the problem is described. This problem arises when determining the places of forest felling when the planned cutting area can be modelled by a rectangle, and the polygons describe the areas with same forest taxation, for each of which is known forest stock per hectare.