Guarding scenes against invasive hypercubes

Mark De Berg, Haggai David, Matthew J. Katz, Mark Overmars, A. Frank Van Der Stappen, Jules Vleugels

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


In recent years realistic input models for geometric algorithms have been studied. The most important models introduced are fatness, low density, unclutteredness and small simple-cover complexity. These models form a strict hierarchy. Unfortunately, small simple-cover complexity is often too general to enable efficient algorithms. In this paper we introduce a new model based on guarding sets. Informally, a guarding set for a collection of objects is a set of points that approximates the distribution of the objects. Any axis-parallel hyper-cube that contains no guards in its interior may intersect at most a constant number of objects. We show that guardable scenes fit in between unclutteredness and small simple-cover complexity. They do enable efficient algorithms, for example a linear size binary space partition. We study properties of guardable scenes and give heuristic algorithms to compute small guarding sets.

Original languageEnglish
Pages (from-to)99-117
Number of pages19
JournalComputational Geometry: Theory and Applications
Issue number2
StatePublished - 1 Oct 2003


  • Epsilon-nets
  • Guarding sets
  • Input models

ASJC Scopus subject areas

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


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