Non-crossing matchings of points with geometric objects
Author(s)Aloupis, Greg; Cardinal, Jean; Collette, Sebastien; Demaine, Erik D.; Demaine, Martin L.; Dulieu, Muriel; Fabila-Monroy, Ruy; Hart, Vi; Hurtado, Ferran; Langerman, Stefan; Saumell, Maria; Seara, Carlos; Taslakian, Perouz; ... Show more Show less
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Given an ordered set of points and an ordered set of geometric objects in the plane, we are interested in finding a non-crossing matching between point–object pairs. In this paper, we address the algorithmic problem of determining whether a non-crossing matching exists between a given point–object pair. We show that when the objects we match the points to are finite point sets, the problem is NP-complete in general, and polynomial when the objects are on a line or when their size is at most 2. When the objects are line segments, we show that the problem is NP-complete in general, and polynomial when the segments form a convex polygon or are all on a line. Finally, for objects that are straight lines, we show that the problem of finding a min-max non-crossing matching is NP-complete.
DepartmentMassachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Aloupis, Greg, Jean Cardinal, Sebastien Collette, Erik D. Demaine, Martin L. Demaine, Muriel Dulieu, Ruy Fabila-Monroy, et al. “Non-Crossing Matchings of Points with Geometric Objects.” Computational Geometry 46, no. 1 (January 2013): 78–92.
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