CONSTRUCTING OPTIMAL HIGHWAYS

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For two points p and q in the plane, a straight 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 hand with speed 1 in the underlying metric elsewhere . Given a set S of n points in the plane and a highway speed v, we consider the problem of finding a highway that minimizes the maximum travel time over all pairs of points in S. If the orientation of the highway is fixed the optimal highway can be computed in linear time both for the L(1)- and the Euclidean metric as the underlying metric. If arbitrary orientations are allowed, then the optimal highway can be computed in O(n(2) log n) time. We also consider the problem of computing an optimal pair of highways, one being horizontal, one vertical.
Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
Issue Date
2009-02
Language
ENG
Article Type
Article
Keywords

CITY VORONOI DIAGRAM; DISTANCES; PATHS

Citation

INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE, v.20, no.1, pp.3 - 23

ISSN
0129-0541
URI
http://hdl.handle.net/10203/16800
Appears in Collection
CS-Journal Papers(저널논문)
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