Abstract
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 \(\overline{pq}\) 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 \(\overline{pq}\) to p, to the Euclidean distance from r to p. We solve this problem in O(λ 7(n)logn) time, where λ 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 (α,β)-covered polygons, a constant number of feed-links suffices to realize constant dilation.
This research has been supported by the Netherlands Organisation for Scientific Research (NWO) under BRICKS/FOCUS grant number 642.065.503, under the project GOGO, and under project no. 639.022.707. B. Aronov has been partially supported by a grant from the U.S.-Israel Binational Science Foundation, by NSA MSP Grant H98230-06-1-0016, and NSF Grant CCF-08-30691. M. Buchin is supported by the German Research Foundation (DFG) under grant number BU 2419/1-1.
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Aronov, B. et al. (2009). Connect the Dot: Computing Feed-Links with Minimum Dilation. In: Dehne, F., Gavrilova, M., Sack, JR., Tóth , C.D. (eds) Algorithms and Data Structures. WADS 2009. Lecture Notes in Computer Science, vol 5664. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03367-4_5
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DOI: https://doi.org/10.1007/978-3-642-03367-4_5
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