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Characterizing and Covering Some Subclasses of Orthogonal Polygons

  • Ana Mafalda Martins
  • António Leslie Bajuelos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3992)

Abstract

A grid n -ogon is a n-vertex orthogonal polygon that may be placed in a \(\frac{n}{2}\times \frac{n}{2}\) unit square grid and that does not have collinear edges. Given a grid n-ogon P, let |Π(P)| be the number of rectangles that results when we partition P by extending the edges incident to reflex vertices towards its interior. P is called Fat if |Π(P)| is maximal for all grid n-ogons; P is called Thin if |Π(P)| is minimal for all grid n-ogons. Thins with area 2r+1 are called Min-Area. We will show that \(\lceil\frac{n}{6}\rceil\) vertex guards are necessary to guard a Min-Area grid n-ogon and present some problems related to Thins.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ana Mafalda Martins
    • 1
  • António Leslie Bajuelos
    • 2
  1. 1.Escola Superior de Ciências e TecnologiaUniversidade Católica PortuguesaPortugal
  2. 2.Dept. of Mathematics & CEOC – Center for Research in Optimization and ControlUniversity of AveiroPortugal

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