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Triangulating and Guarding Realistic Polygons G. Aloupis P. Bose V. Dujmovic C. Gray S. Langerman B. Speckmann
 

Summary: Triangulating and Guarding Realistic Polygons
G. Aloupis P. Bose V. Dujmovic C. Gray § S. Langerman ¶ B. Speckmann §
Abstract
We propose a new model of realistic input: k-guardable objects. An object is k-guardable if
its boundary can be seen by k guards. We show that k-guardable polygons generalize two
previously identified classes of realistic input. Following this, we give two simple algorithms
for triangulating k-guardable polygons. One algorithm requires the guards as input while
the other does not. Both take linear time assuming that k is constant and both are easily
implementable.
1 Introduction
Algorithms and data structures in computational geometry often display their worst-case per-
formance on intricate input configurations that seem artificial or unrealistic when considered in
the context of the original problem. Indeed, in "practical" situations, many algorithms and data
structures--binary space partitions are a notable example--tend to perform much better than
predicted by the theoretical bounds. An attempt to understand this disparity and to quantify
"practical" or "normal" with respect to input are the so-called realistic input models [7]. Here
one places certain restrictions on the shape and/or distribution of the input objects so that
most unusual hypothetical worst-case examples are excluded. Analyzing the algorithm or data
structure in question under these input assumptions tends to lead to performance bounds that
are much closer to actually observed behavior.

  

Source: Aloupis, Greg - Département d'Informatique, Université Libre de Bruxelles

 

Collections: Mathematics; Computer Technologies and Information Sciences