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Quasi-Parallel Segments and Characterization of Unique Bichromatic Matchings (1302.4400v1)
Published 18 Feb 2013 in cs.CG
Abstract: Given n red and n blue points in general position in the plane, it is well-known that there is a perfect matching formed by non-crossing line segments. We characterize the bichromatic point sets which admit exactly one non-crossing matching. We give several geometric descriptions of such sets, and find an O(nlogn) algorithm that checks whether a given bichromatic set has this property.