Routing in polygonal domains

Abstract 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 e > 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 + e . The labels have O ( log ⁡ n ) bits, and the routing tables are of size O ( ( e − 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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