Abstract
Consider a weighted graph G whose vertices are points in the plane and edges are line segments between pairs of points whose weight is the Euclidean distance between its endpoints. A routing algorithm on G sends a message from any vertex s to any vertex t in G. The algorithm has a competitive ratio of c if the length of the path taken by the message is at most c times the length of the shortest path from s to t in G. It has a routing ratio of c if the length of the path is at most c times the Euclidean distance from s to t. The algorithm is online if it makes forwarding decisions based on (1) the k-neighborhood in G of the message’s current position (for constant k > 0) and (2) limited information stored in the message header.
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