TY - GEN

T1 - Connect the dot

T2 - 11th International Symposium on Algorithms and Data Structures, WADS 2009

AU - Aronov, Boris

AU - Buchin, Kevin

AU - Buchin, Maike

AU - Van Kreveld, Marc

AU - Löffler, Maarten

AU - Luo, Jun

AU - Silveira, Rodrigo I.

AU - Speckmann, Bettina

PY - 2009

Y1 - 2009

N2 - 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(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.

AB - 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(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.

UR - http://www.scopus.com/inward/record.url?scp=69949190087&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=69949190087&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-03367-4_5

DO - 10.1007/978-3-642-03367-4_5

M3 - Conference contribution

AN - SCOPUS:69949190087

SN - 3642033660

SN - 9783642033667

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 49

EP - 60

BT - Algorithms and Data Structures - 11th International Symposium, WADS 2009, Proceedings

Y2 - 21 August 2009 through 23 August 2009

ER -