《贪婪和德劳内一样好》（Greedy is as Good as Delaunay）
Greedy is as Good as Delaunay (Almost)
摘要：
设S是平面点集。Krznaric和Levcopoulos证明了给定S的德洛内三角剖分DT（S），可以在线性时间内找到贪婪三角剖分GT（S）。我们提供了这个结果的（部分）逆：给定GT（S），可以在线性期望时间内计算DT（S）。因此，这些结构基本上是等同的。为了得到我们的结果，我们推广了Krznaric和Levcopoulos的另一种算法，一旦DT（S）已知，就可以在线性时间内找到S的层次聚类。我们表明，他们的算法仍然（几乎）正确的任何三角有界扩张，即，任意两点之间的最短路径距离接近它们的欧几里得距离的三角剖分。然而，一般来说，所得到的运行时间可能是超线性的。尽管如此，我们可以证明贪婪三角剖分的性质足以保证线性时间界。
英文摘要：
Let S be a planar point set. Krznaric and Levcopoulos proved that given the Delaunay triangulation DT(S) for S, one can find the greedy triangulation GT(S) in linear time. We provide a (partial) converse of this result: given GT(S), it is possible to compute DT(S) in linear expected time. Thus, these structures are basically equivalent. To obtain our result, we generalize another algorithm by Krznaric and Levcopoulos to find a hierarchical clustering for S in linear time, once DT(S) is known. We show that their algorithm remains (almost) correct for any triangulation of bounded dilation, i.e., any triangulation in which the shortest path distance between any two points approximates their Euclidean distance. In general, however, the resulting running time may be superlinear. Nonetheless, we can show that the properties of the greedy triangulation suffice to guarantee a linear time bound.
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。
