Quasi-parallel segments and characterization of unique bichromatic matchings

Andrei Asinowski, Tillmann Miltzow, Günter Rote


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(n log n) algorithm that checks whether a given bichromatic set has this property.

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DOI: http://dx.doi.org/10.20382/jocg.v6i1a8

ISSN: 1920-180X