Approximating Watchman Routes

Given a connected polygonal domain P, the watchman route problem is to compute a shortest path or tour for a mobile guard (the "watchman") that is required to see every point of P. While the watchman route problem is polynomially solvable in simple polygons, it is known to be NP-hard in polygons with holes. We present the first polynomial-time approximation algorithm for the watchman route problem in polygonal domains. Our algorithm has an approximation factor O(log(2) n). Further, we prove that the problem cannot be approximated in polynomial time to within a factor of c log n, for a constant c > 0, assuming that P not equal NP.