Linear time algorithm for optimal feed-link placement

摘要

Given a polygon representing a transportation network together with a point p in its interior, we aim to extend the network by inserting a line segment, called feed-link, which connects p to the boundary of the polygon. Once a feed link is fixed, the geometric dilation of some point q on the boundary is the ratio between the length of the shortest path from p to q through the extended network, and their Euclidean distance. The utility of a feed-link is inversely proportional to the maximal dilation over all boundary points.