Given a polygon $P$, the art gallery problem looks to find a smallest set of points that sees all of $P$. One way of bounding the number of guards necessary (from below) is to find a largest set of independent witness points, which are points whose visibility polygons are pairwise disjoint. Say the size of the smallest guarding set is $G(P)$ and the size of the largest witness set is $W(P)$. Then we have the trivial lower bound on $G(P)$, that $W(P) \leq G(P)$.

In arbitrary polygons, the size of the witness set does not help much with respect to an upper bound on the size of the guard set, i.e. there are examples with $\frac{G(P)}{W(P)} = \Omega(n)$.

Does the same hold for orthogonal polygons? It seems plausible to me that, unlike general polygons, a constant factor bound exists (maybe $\frac{G(P)}{W(P)} \leq 2$?), but my literature search came up empty. Can anyone point me at a reference, or a bad example?

guard setis a set of points such that every point in $P$ is connected to some point in the set by a segment that is nowhere exterior to $P$. $\endgroup$ – Joseph O'Rourke Jun 25 '13 at 23:289more comments