Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Voronoi Diagram for services neighboring a highway
Information Processing Letters
Shortest paths and voronoi diagrams with transportation networks under general distances
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Voronoi diagrams with a transportation network on the euclidean plane
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Optimal location of transportation devices
Computational Geometry: Theory and Applications
Optimal Insertion of a Segment Highway in a City Metric
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
All Farthest Neighbors in the Presence of Highways and Obstacles
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Computational Geometry: Theory and Applications
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For two points p and q in the plane, a (unbounded) line h, called a highway, and a real v 1, we define the travel time (also known as the city distance) from p and q to be the time needed to traverse a quickest path from p to q, where the distance is measured with speed v on h and with speed 1 in the underlying metric elsewhere. Given a set S of n points in the plane and a high-way speed v, we consider the problem of finding an axis-parallel line, the highway, that minimizes the maximum travel time over all pairs of points in S. We achieve a linear-time algorithm both for the L1- and the Euclidean metric as the underlying metric. We also consider the problem of computing an optimal pair of highways, one being horizontal, one vertical.