Before revision:  In this paper , we present the first routing scheme for the particular case in which the network is defined by the visibility graph of a polygon with n vertices and h holes. For any \varepsilon > 0 the routing scheme provides stretch at most 1 + \varepsilon.
After revision:  In this paper , we present a routing scheme that always achieves a routing path whose length exceeds the shortest path by a factor of at most 1 + \varepsilon.