Guarding Scenes against Invasive Hypercubes

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 axisparallel 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.

• Type: Conference
• Year: 1998
• Where: WAE
• Authors: Mark de Berg, Haggai David, Matthew J. Katz, Mark H. Overmars, A. Frank van der Stappen, Jules Vleugels
• Keywords: Enable Efficient Algorithms, Realistic Input Models, Small Simple-cover Complexity, WAE 1998, WAE 2001