New results on stabbing segments with a polygon

José Miguel Díaz-Báñez, Matias Korman, Pablo Pérez-Lantero, Alexander Pilz, Carlos Seara, Rodrigo I. Silveira

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

We consider a natural variation of the concept of stabbing a set of segments with a simple polygon: a segment s is stabbed by a simple polygon P if at least one endpoint of s is contained in P, and a segment set S is stabbed by P if P stabs every element of S. Given a segment set S, we study the problem of finding a simple polygon P stabbing S in a way that some measure of P (such as area or perimeter) is optimized. We show that if the elements of S are pairwise disjoint, the problem can be solved in polynomial time. In particular, this solves an open problem posed by Löffler and van Kreveld [Algorithmica 56(2), 236-269 (2010)] [16] about finding a maximum perimeter convex hull for a set of imprecise points modeled as line segments. Our algorithm can also be extended to work for a more general problem, in which instead of segments, the set S consists of a collection of point sets with pairwise disjoint convex hulls. We also prove that for general segments our stabbing problem is NP-hard.

Original languageEnglish
Pages (from-to)14-29
Number of pages16
JournalComputational Geometry: Theory and Applications
Volume48
Issue number1
DOIs
Publication statusPublished - 2015 Jan

Keywords

  • Imprecise points
  • Segments
  • Stabber
  • Transversal

ASJC Scopus subject areas

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics

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