Computational complexity of art gallery problems
IEEE Transactions on Information Theory
Art gallery theorems and algorithms
Art gallery theorems and algorithms
Solving some combinatorial problems in grid n-ogons
ACS'07 Proceedings of the 7th Conference on 7th WSEAS International Conference on Applied Computer Science - Volume 7
Polygons Drawn from Permutations
Fundamenta Informaticae - Strategies for Tomography
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A grid n-ogon is a n-vertex orthogonal polygon that may be placed in a $\frac{n}{2}\times \frac{n}{2}$ unit square grid and that does not have collinear edges. Given a grid n-ogon P, let |Π(P)| be the number of rectangles that results when we partition P by extending the edges incident to reflex vertices towards its interior. P is called Fat if |Π(P)| is maximal for all grid n-ogons; P is called Thin if |Π(P)| is minimal for all grid n-ogons. Thins with area 2r+1 are called Min-Area. We will show that $\lceil\frac{n}{6}\rceil$ vertex guards are necessary to guard a Min-Area grid n-ogon and present some problems related to Thins.