Connect the dot: Computing feed-links with minimum dilation

B. Aronov, K. Buchin, M. Buchin, M.J. Kreveld, van, M. Löffler, J. Luo, R.I. Silveira, B. Speckmann

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

2 Citations (Scopus)
1 Downloads (Pure)


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.
Original languageEnglish
Title of host publicationAlgorithms and Data Structures (Proceedings 11th International Workshop, WADS 2009, Banff, Alberta, Canada, August 21-23, 2009)
EditorsF. Dehne, M. Gavrilova, J.-R. Sack, C.D. Tóth
Place of PublicationBerlin
ISBN (Print)978-3-642-03366-7
Publication statusPublished - 2009

Publication series

NameLecture Notes in Computer Science
ISSN (Print)0302-9743


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