Non-crossing matchings of points with geometric objects
Name
Demaine_Non-crossing matches.pdf
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468.02 KB
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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
Date Issued
April 2012
Journal
Computational Geometry
Publisher
Elsevier
Citation
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.
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-Noncommercial-NoDerivatives
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/j.comgeo.2012.04.005
