volume 33, issue 2, P345-364 2004
DOI: 10.1007/s00454-004-1091-9
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Abstract: We use the concept of pointed pseudo-triangulations to establish new upper and lower bounds on a well known problem from the area of art galleries: What is the worst case optimal number of vertex π-guards that collectively monitor a simple polygon with n vertices? Our results are as follows:1. Any simple polygon with n vertices can be monitored by at most n/2 general vertex π-guards. This bound is tight up to an additive constant of 1. 2. Any simple polygon with n vertices, k of which are convex, can be monit…

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