d维随机点Delaunay图最长边长度的概率界
Probabilistic Bounds on the Length of a Longest Edge in Delaunay Graphs of Random Points in d-Dimensions
摘要：
受无线网络中地理路由的低能耗的启发，最近人们对确定随机分布点的Delaunay图中的边的长度的界限感兴趣。平面域中随机网络的渐近结果是已知的。本文对有界和无界区域中随机均匀分布的点，得到了在任意维上参数概率成立的上、下界。得到的结果是渐近紧的所有相关值的概率和常数的维数，并表明，在平面中的边界节点产生的开销也持有更高的维度。据我们所知，这是第一次对Delaunay图的长边长度进行全面的研究
英文摘要：
Motivated by low energy consumption in geographic routing in wireless networks, there has been recent interest in determining bounds on the length of edges in the Delaunay graph of randomly distributed points. Asymptotic results are known for random networks in planar domains. In this paper, we obtain upper and lower bounds that hold with parametric probability in any dimension, for points distributed uniformly at random in domains with and without boundary. The results obtained are asymptotically tight for all relevant values of such probability and constant number of dimensions, and show that the overhead produced by boundary nodes in the plane holds also for higher dimensions. To our knowledge, this is the first comprehensive study on the lengths of long edges in Delaunay graphs
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。
