Sending a message through an unknown network is a difficult problem. In this paper, we consider the case in which, during a preprocessing phase, we assign a label and a routing table to each node. The routing strategy must then decide where to send the package using only the label of the target node  and the routing table of the node the message is currently at. 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. The labels have O(\log n) bits and the corresponding routing tables are of size O( \varepsilon^{-1 + 1 )\log n). The preprocessing time is O(n^2\log n +(h+1)n^2+\varepsilon^{-1 can be improved to O(n^2 +\varepsilon^{-1 ) for simple polygons.
We consider the problem of routing a data packet through the visibility graph of a polygonal domain P with n vertices and h holes. We may preprocess P to obtain a label and a routing table for each vertex of P. Then, we must be able to route a data packet between any two vertices p and q of P, where each step must use only the label of the target node q and the routing table of the current node. For any fixed \varepsilon > 0 , 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. The labels have O(\log n) bits , and the routing tables are of size O( (\varepsilon^{-1 + h )\log n). The preprocessing time is O(n^2\log n ). It can be improved to O(n^2 ) for simple polygons.
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