Sharp upper and lower bounds on the length of general Davenport-Schinzel Sequences
Journal of Combinatorial Theory Series A
Finding the upper envelope of n line segments in O(n log n) time
Information Processing Letters
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
On fat partitioning, fat covering and the union size of polygons
Computational Geometry: Theory and Applications
Approximating the Stretch Factor of Euclidean Graphs
SIAM Journal on Computing
Computing the Maximum Detour and Spanning Ratio of Planar Paths, Trees, and Cycles
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Finding the best shortcut in a geometric network
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
The Complexity of the Union of $(\alpha,\beta)$-Covered Objects
SIAM Journal on Computing
The Geometric Dilation of Finite Point Sets
Algorithmica
Geometric Spanner Networks
Feed-links for network extensions
Proceedings of the 16th ACM SIGSPATIAL international conference on Advances in geographic information systems
Local polyhedra and geometric graphs
Computational Geometry: Theory and Applications - Special issue on the 19th annual symposium on computational geometry - SoCG 2003
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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 (*** 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 (*** ,β )-covered polygons, a constant number of feed-links suffices to realize constant dilation.