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 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 to p, to the Euclidean distance from r to p. We solve this problem in O(¿ 7(n)logn) time, where ¿ 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 (a,ß)-covered polygons, a constant number of feed-links suffices to realize constant dilation.
|Title of host publication||Algorithms and Data Structures (Proceedings 11th International Workshop, WADS 2009, Banff, Alberta, Canada, August 21-23, 2009)|
|Editors||F. Dehne, M. Gavrilova, J.-R. Sack, C.D. Tóth|
|Place of Publication||Berlin|
|Publication status||Published - 2009|
|Name||Lecture Notes in Computer Science|