New Results on Stabbing Segments with a Polygon

  • José Miguel Díaz-Báñez
  • Matias Korman
  • Pablo Pérez-Lantero
  • Alexander Pilz
  • Carlos Seara
  • Rodrigo I. Silveira
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7878)

Abstract

We consider a natural variation of the concept of stabbing a segment by a simple polygon: a segment is stabbed by a simple polygon \(\mathcal{P}\) if at least one of its two endpoints is contained in \(\mathcal{P}\). A segment set S is stabbed by \(\mathcal{P}\) if every segment of S is stabbed by \(\mathcal{P}\). We show that if S is a set of pairwise disjoint segments, the problem of computing the minimum perimeter polygon stabbing S can be solved in polynomial time. We also prove that for general segments the problem is NP-hard. Further, an adaptation of our polynomial-time algorithm solves an open problem posed by Löffler and van Kreveld [Algorithmica 56(2), 236–269 (2010)] about finding a maximum perimeter convex hull for a set of imprecise points modeled as line segments.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • José Miguel Díaz-Báñez
    • 1
  • Matias Korman
    • 2
  • Pablo Pérez-Lantero
    • 3
  • Alexander Pilz
    • 4
  • Carlos Seara
    • 2
  • Rodrigo I. Silveira
    • 2
  1. 1.Dept. Matemática Aplicada IIUniversidad de SevillaSpain
  2. 2.Dept. Matemàtica Aplicada IIUniversitat Politècnica de CatalunyaSpain
  3. 3.Escuela de Ingeniería Civil en InformáticaUniversidad de ValparaísoChile
  4. 4.Institute for Software TechnologyGraz University of TechnologyAustria

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