Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4949162 | Computational Geometry | 2016 | 13 Pages |
Abstract
We prove that every simply connected orthogonal polygon of n vertices can be partitioned into â3n+416â (simply connected) orthogonal polygons of at most 8 vertices. It yields a new and shorter proof of the theorem of A. Aggarwal that â3n+416â mobile guards are sufficient to control the interior of an n-vertex orthogonal polygon. Moreover, we strengthen this result by requiring combinatorial guards (visibility is only needed at the endpoints of patrols) and prohibiting intersecting patrols. This yields positive answers to two questions of O'Rourke [7, Section 3.4]. Our result is also a further example of the “metatheorem” that (orthogonal) art gallery theorems are based on partition theorems.
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Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Ervin GyÅri, Tamás Róbert Mezei,