Abstract
This paper considers the following geometric optimization problem: Input is a matrix R=(r ij ). Each entry r ij represents a radius of a disc with its center at (i,j) in the plane. We want to choose discs in such a way that the total area covered by exactly one disc is maximized. This problem is closely related to digital halftoning, a technique to convert a continuous-tone image into a binary image for printing. An exact algorithm is given for the one-dimensional version of the problem while approximation algorithms are given for the two-dimensional one. The approximation algorithms are verified to be satisfactory in practice through experiments in applications to digital halftoning.
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Asano, T., Brass, P. & Sasahara, S. Disc Covering Problem with Application to Digital Halftoning. Theory Comput Syst 46, 157–173 (2010). https://doi.org/10.1007/s00224-008-9123-0
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DOI: https://doi.org/10.1007/s00224-008-9123-0