Abstract.We propose an anytime algorithm to compute successively better approximations of the optimum of Minimum Vertex Guard. Though the presentation is focused on polygons, the work may be directly extended to terrains along the lines of [4]. A major idea in our approach is to explore dominance of visibility regions to first detect pieces that are more difficult to guard.

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Abstract. We propose two different methods for generating random orthogonal polygons with a given number of vertices. One is a polynomial time algorithm and it is supported by a technique we developed to obtain polygons with an increasing number of vertices starting from a unit square. The other follows a constraint programming approach and gives great control on the generated polygons. In particular, it may be used to find all n-vertex orthogonal polygons with no collinear edges that can be drawn in angrid, for small n, with symmetries broken.

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