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Matching Points with Things

  • Greg Aloupis
  • Jean Cardinal
  • Sébastien Collette
  • Erik D. Demaine
  • Martin L. Demaine
  • Muriel Dulieu
  • Ruy Fabila-Monroy
  • Vi Hart
  • Ferran Hurtado
  • Stefan Langerman
  • Maria Saumell
  • Carlos Seara
  • Perouz Taslakian
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6034)

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. 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.

Keywords

Line Segment Computational Geometry Convex Polygon Strong Connected Component Matching Edge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Greg Aloupis
    • 1
  • Jean Cardinal
    • 1
  • Sébastien Collette
    • 1
  • Erik D. Demaine
    • 2
  • Martin L. Demaine
    • 2
  • Muriel Dulieu
    • 3
  • Ruy Fabila-Monroy
    • 4
  • Vi Hart
    • 5
  • Ferran Hurtado
    • 6
  • Stefan Langerman
    • 1
  • Maria Saumell
    • 6
  • Carlos Seara
    • 6
  • Perouz Taslakian
    • 1
  1. 1.Université Libre de BruxellesBrusselsBelgium
  2. 2.MIT Computer Science and Artificial Intelligence LaboratoryCambridgeUSA
  3. 3.Polytechnic Institute of NYUUSA
  4. 4.Instituto de MatemáticasUniversidad Nacional Autónoma de México 
  5. 5.Stony Brook UniversityStony BrookUSA
  6. 6.Universitat Politècnica de CatalunyaBarcelonaSpain

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