公路船体再访
Highway Hull Revisited
摘要：
公路H是平面上的一条线，在这条线上，人们可以以比在其余平面上更大的速度行驶。可以选择在任何点进入和退出H。一对点之间的公路时间距离是从一个点移动到另一个点所需的最短时间，可选择使用H。点集S的公路包HH（S，H）是包含S以及HH（S，H）中所有点对之间的最短路径的最小集合，使用公路时间距离。在L_1度量下，我们给出了一个Theta（nlogn）的最坏情况时间算法，在L_2度量下，我们给出了一个O（nlog^2n）的时间算法，改进了O（n^2）的已知结果.我们还定义并构造了平面的有用区域：公路必须相交的区域，以便至少一对点之间的最短路径使用公路。
英文摘要：
A highway H is a line in the plane on which one can travel at a greater speed than in the remaining plane. One can choose to enter and exit H at any point. The highway time distance between a pair of points is the minimum time required to move from one point to the other, with optional use of H. The highway hull HH(S,H) of a point set S is the minimal set containing S as well as the shortest paths between all pairs of points in HH(S,H), using the highway time distance. We provide a Theta(n log n) worst-case time algorithm to find the highway hull under the L_1 metric, as well as an O(n log^2 n) time algorithm for the L_2 metric which improves the best known result of O(n^2). We also define and construct the useful region of the plane: the region that a highway must intersect in order that the shortest path between at least one pair of points uses the highway.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
