Guarding Galleries with No Nooks (extended Abstract)
نویسنده
چکیده
We consider the problem of guarding galleries that have no small nooks (regions that are visible from only a small fraction of the entire gallery). Intuitively, such galleries (of which convex galleries are a special but uninteresting case) should need fewer guards. We show that in any simply connected gallery in which every corner sees at least a fraction of the other corners there exist a set of at most 64 1 log log 1 corners (guard stations) from which every other corner is visible. Similar results also hold for guarding the entire boundary with guards stationed at points on the boundary. These results are similar but slightly stronger than analogous results known for guarding the interior of a gallery. We provide a direct and simple guard assignment scheme that realizes the size bounds.
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