Optimal circle covering problems and their applications

We study a special type of circle covering problem, the complete cover of polygons by not necessarily congruent circles with prescribed centres. We introduce a branch-and-bound algorithm which is able to check whether an actual set of circles covers a given polygon. Furthermore, we present a method capable of finding the optimal cover with arbitrary precision. These techniques are based on interval arithmetic, therefore our results are numerically reliable. To demonstrate the performance of the developed optimization method, we determine the optimal cover of the unit square and an irregular polygon.