加权区域上的Fréchet距离问题
Fréchet Distance Problems in Weighted Regions
摘要：
我们讨论两个版本的加权平面细分的Fréchet距离问题。在第一种情况下，两点之间的距离是连接两点的线段的加权长度。在第二种情况下，两点之间的距离是两点之间的最短路径的长度。在这两种情况下，我们给出了算法，找到一个（1+ 1）-因子近似的Fréchet距离两个多边形曲线之间。我们还考虑了R^3中多面体障碍物间两条多边形曲线之间的Fréchet距离，并提出了一种（1+ λ）因子近似算法。
英文摘要：
We discuss two versions of the Fréchet distance problem in weighted planar subdivisions. In the first one, the distance between two points is the weighted length of the line segment joining the points. In the second one, the distance between two points is the length of the shortest path between the points. In both cases, we give algorithms for finding a (1+epsilon)-factor approximation of the Fréchet distance between two polygonal curves. We also consider the Fréchet distance between two polygonal curves among polyhedral obstacles in R^3 and present a (1+epsilon)-factor approximation algorithm.
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