MODEL OF THE MAXIMUM COVERAGE OF A PARTICULAR AREA TAKING INTO ACCOUNT OF SPECIAL-LOOK RESTRICTIONS

Abstract

The task of optimal coverage of a given area (in our case, it is a convex polygon with a certain set of sub-areas of coverage) is to determine the minimum number of coverage objects, taking into account the constraints that affect the amount of data objects.

In two-dimensional space, the coverage of a given area is usually made by circles of a given radius, rectangles, polygons, objects with variable metric characteristics, and the like.

In this paper, we have developed a mathematical model for covering a given area by convex polygons with variable metric characteristics, taking into account the following limitations: minimum cross-sectional area of the coverage objects; minimum area of ​​intersection of coverage objects and addition of a given area to two-dimensional space; the placement parameters of the coverage objects must be points in the specified subregions, taking into account the priority subregions; the maximum coverage of the specified subregions of the corresponding objects; the relevance of the specified subregions to the coverage objects; the prioritization of subregions for the intersection of a given number of coverage objects; special-type restrictions that affect the metric characteristics of coverage objects.

The resulting model allows us to develop a valid method of geometric modeling of maximum coverage and to perform computer simulation of the coverage of a given area, taking into account the limitations of the special type.

Further research will be directed to solving other problems arising from the general formulation and to developing methods of geometric optimization.

Keywords: maximum coverage, special type restriction, general model, given area, subregions.