- 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 epsilon > 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 + epsilon. The labels have O(log n) bits, and the routing tables are of size O(((epsilon^-1)+h)log n). The preprocessing time is O((n^2)log n). It can be improved to O(n^2) for simple polygons.