Abstract
Given a set R of m disjoint finite regions in the 2-dimensional plane, all regions having polygonal boundaries, and given a set D of n discs with fixed centers and radii, we consider the problem of finding a minimum cardinality subset D∗⊆D such that every point in R is covered by at least one disc in D∗. We show that this problem can be solved by using an iterative procedure that alternates between the solution of a traditional set-cover problem and the construction of the Laguerre–Voronoi diagram of a circle set. Computer experiments demonstrate the effectiveness of the proposed algorithm, particularly when the number |D∗| of discs necessary to cover R is low.
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