Solving some combinatorial problems in grid n-ogons

In this paper we study some problems related to grid n-ogons. A grid n-ogon is a n-vertex orthogonal simple polygon, with no collinear edges, that may be placed in a (n/2) × (n/2) square grid. We will present some problems and results related to a subclass of grid n-ogons, the THIN grid n-ogons, in particular a classification for this subclass of polygons. We follow by presenting the solution of the MINIMUM VERTEX GUARD problem for the MIN-AREA and for the SPIRAL grid n-ogons. Finally the solution of the MAXIMUM HIDDEN VERTEX SET problem for THIN grid n-ogons is also presented.