Guarding simple polygons with semi-open edge guards

Let bd(P ) denote the boundary of a simple polygon P . Points p and q of P are mutually visible if segment pq lies entirely inside P . This notion of visibility gave birth to an extensive literature on art-gallery problems [3], concerned with guarding the floor of a polygonal art-gallery. Chvatal [2] showed that bn/3c point guards are always sufficient and sometimes necessary. Allowing guards to move on an edge gives rise to the class of edge guard problems. An edge guard is closed (open) if the end-points of the edge are included (excluded), semi-open if only one end-point is included. Shermer [5] established an upper bound of b3n/10c + 1 on the number of closed edge guards needed, while Toussaint [3] showed that bn/4c guards are sometimes necessary. A guard edge is one that guards all of P . In [6], Toth et al. have shown that a non star-shaped simple polygon has at most one open guard edge. Park et al. [4] showed that such a polygon can have at most 3 closed guard edges.