The Cover Contact Graph of Discs Touching a Line
نویسندگان
چکیده
We answer a question of Atienza et al. [4] by showing that the circular CCG problem is NP-complete. If we cover a set of objects on the plane with discs whose interiors are pairwise disjoint, then we can form a cover contact graph (CCG) that records which of the covering discs touch at their boundaries. When the input objects are themselves discs, and both input and covering discs are constrained to be touching and above the x-axis, then the circular CCG problem is to decide the existence of a covering with a connected CCG. We also define an approximate version of this problem by allowing a small overlap between covering discs, and give an algorithm that in polynomial time finds an approximate solution for any yes-instance of the exact problem.
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