A feed-link is an artificial connection from a given location p to a real world network. It is most commonly added to an incomplete network to improve the results of network analysis, by making p part of the network. The feed-link has to be reasonable, hence we use the concept of dilation to determine the quality of a connection. We consider the following abstract problem: Given a simple polygon P with n vertices and a point p inside, determine a point q on P such that adding a feedlink pq minimizes the maximum dilation of any point on P. Here the dilation of a point r on P is the ratio of the shortest route from r over P and pq to p, to the Euclidean distance from r to p. We solve this problem in O(lambda_7(n) log n) time, where lambda_7(n) is the slightly superlinear maximum length of a Davenport-Schinzel sequence of order 7. We also show that for convex polygons, two feed-links are always sufficient and sometimes necessary to realize constant dilation, and that k feed-links lead to a dilation of 1+O(1/k). For (alpha,beta)-covered polygons, a constant number of feed-links suffices to realize constant dilation.
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