Routing in Polygonal Domains

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. 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 that exceeds the shortest path by a factor of at most $1 + . The labels have $O(log n)$ bits, and the routing tables are of size $O((-1+h)log n)$. The preprocessing time is $O(n^2log n + hn^2+-1hn)$. It can be improved to $O(n^2+-1n)$ for simple polygons.