Matching Points with Things
Author(s)Aloupis, Greg; Cardinal, Jean; Collette, Sebastien; Dulieu, Muriel; Fabila-Monroy, Ruy; Hart, Vi; Hurtado, Ferran; Langerman, Stefan; Saumell, Maria; Seara, Carlos; Taslakian, Perouz; Demaine, Erik D.; Demaine, Martin L.; ... 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. 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 number 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
LATIN 2010: Theoretical Informatics 9th Latin American Symposium, Oaxaca, Mexico, April 19-23, 2010. Proceedings
Springer Berlin / Heidelberg
Aloupis, Greg et al. “Matching Points with Things.” LATIN 2010: Theoretical Informatics. Ed. Alejandro López-Ortiz. Vol. 6034. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. 456–467. Web. 25 June 2012.
Author's final manuscript