Planar point location using persistent search trees
Communications of the ACM
Planar geometric location problems and maintaining the width of a planar set
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Geometric applications of a randomized optimization technique
Proceedings of the fourteenth annual symposium on Computational geometry
Optimal point placement for mesh smoothing
Journal of Algorithms
Faster construction of planar two-centers
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
A practical approach for computing the diameter of a point set
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Quickest paths, straight skeletons, and the city Voronoi diagram
Proceedings of the eighteenth annual symposium on Computational geometry
Voronoi Diagram for services neighboring a highway
Information Processing Letters
An optimal randomized algorithm for maximum Tukey depth
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
CATS '07 Proceedings of the thirteenth Australasian symposium on Theory of computing - Volume 65
An optimal randomized algorithm for d-variate zonoid depth
Computational Geometry: Theory and Applications
Computational Geometry: Theory and Applications
Bichromatic 2-center of pairs of points
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
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We consider algorithms for finding the optimal location of a simple transportation device, that we call a moving walkway, consisting of a pair of points in the plane between which the travel speed is high. More specifically, one can travel from one endpoint of the walkway to the other at speed v1, but can only travel at unit speed between any other pair of points. The travel time between any two points in the plane is the minimum between the actual geometric distance, and the time needed to go from one point to the other using the walkway. A location for a walkway is said to be optimal with respect to a given finite set of points if it minimizes the maximum travel time between any two points of the set. We give a simple linear-time algorithm for finding an optimal location in the case where the points are on a line. We also give an @W(nlogn) lower bound for the problem of computing the travel time diameter of a set of n points on a line with respect to a given walkway. Then we describe an O(nlogn) algorithm for locating a walkway with the additional restriction that the walkway must be horizontal. This algorithm is based on a recent generic method for solving quasiconvex programs with implicitly defined constraints. It is used in a (1+@e)-approximation algorithm for optimal location of a walkway of arbitrary orientation.