Minimally covering a horizontally convex orthogonal polygon
SCG '86 Proceedings of the second annual symposium on Computational geometry
Art gallery theorems and algorithms
Art gallery theorems and algorithms
Covering a simple orthogonal polygon with a minimum number of orthogonally convex polygons
SCG '87 Proceedings of the third annual symposium on Computational geometry
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The art gallery theorem: its variations, applications and algorithmic aspects
The art gallery theorem: its variations, applications and algorithmic aspects
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Some NP-hard polygon decomposition problems
IEEE Transactions on Information Theory
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We consider the problem of covering simple orthogonal polygons with star polygons. A star polygon contains a point p, such that for every point q in the star polygon, there is an orthogonally convex polygon containing p and q.In general, orthogonal polygons can have concavities (dents) with four possible orientations. In this case, we show that the polygon covering problem can be reduced to the problem of covering a weakly triangulated graph with a minimum number of cliques. We thus obtain a &Ogr; (n10) algorithm. Since weakly triangulated graphs are perfect, we also obtain an interesting duality relationship.In the case where the polygon has at most three dent orientations, we show that the polygon covering problem can be reduced to the problem of covering a triangulated (chordal) graph with a minimum number of cliques. This gives us an &Ogr; (n3) algorithm.