Constructing Optimal Axis-Parallel Highways
نویسندگان
چکیده
In this paper we consider the problem of constructing optimal highways. For two points p and q in the plane, a line h—the 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 distances are measured in the Manhattan (i.e. the L1-) metric, and the speed on h is v and elsewhere 1. Given a set S of n points in the plane and a highway speed v, we show how to find an axis-parallel line that minimizes the maximum travel time over all pairs of vertices. Our algorithms takes O(n logn) time. We also show that placing k parallel highways does not reduce the maximum travel time.
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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 h and with speed 1 in the underlying metric elsewhere. Given a set S of n points in the plane and a highway speed v, we co...
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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 h and with speed 1 in the underlying metric elsewhere. Given a set S of n points in the plane and a highway speed v, we co...
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