Conversion of a Digital Object into a Finite Set of Balls: Complexity
Résumé
This paper adresses the problem of converting a 2D digital S (a finite set of points in Z2) into a finite set B of balls centered on R2, such that the balls of B cover all points of S and no point of Z2S, and the cardinality of B is minimum. In a precious work, we showed that the problem was polymonial for the specific class of 2D hole-free digital objects. In this article, we show the problem is NP-complete in the general case using a reduction from the 3-Planar Vertex Cover problem.
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