 
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: kguardable objects. An object is kguardable if
its boundary can be seen by k guards. We show that kguardable polygons generalize two
previously identified classes of realistic input. Following this, we give two simple algorithms
for triangulating kguardable 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 worstcase 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
structuresbinary space partitions are a notable exampletend 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 socalled realistic input models [7]. Here
one places certain restrictions on the shape and/or distribution of the input objects so that
most unusual hypothetical worstcase 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.
