A New Algorithm for Guarding

In this paper, we present a new algorithm for vertex guarding of a triangulated surface, which takes into account the heights of the vertices and considers the global visibility of the guards. In this algorithm, the initial surface is reduced to a collection of simple polygons and trivial triangulated surfaces. This is done by assigning guards to some vertices and removing the faces covered by these guards. The remaining simple regions are then guarded properly. The running time of our algorithm is linear in terms of n, the number of vertices. The upper bound of the assigned guards is   3 / 2n , and its expected number is   2 / n , which is the same as the worst case lower bound for the problem. The running time of the best known algorithm for this problem is ) ( 2 / 3 n O which selects at most   2 / n guards. We expect a better performance of our algorithm on the average in practice. This has been verified by experimentation.