Guarding Scenes against Invasive Hypercubes
نویسندگان
چکیده
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.
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