Quasi-Parallel Segments and Characterization of Unique Bichromatic Matchings
arXiv:1302.4400 · doi:10.20382/jocg.v6i1a8
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.
31 pages, 24 figures