关于随机点集干涉的一个注记
A Note on Interference in Random Point Sets
摘要：
研究了几何图形（von Rickenbach等人（2005））的（最大接收器中心）干扰。对于单位d-立方体中独立均匀分布的n个点的集合V，当维数d为常数时，下列结果以很高的概率成立：（1）存在一个顶点集为V的连通图，它的干涉量为O（（log n）^{1/3}），（2）顶点集为V的连通图不存在干涉量为O（（log n）^{1/4}）;以及（3）$V$的最小生成树具有干扰Theta（（\log n）^{1/2}）。
英文摘要：
The (maximum receiver-centric) interference of a geometric graph (von Rickenbach etal (2005)) is studied. It is shown that, with high probability, the following results hold for a set, V, of n points independently and uniformly distributed in the unit d-cube, for constant dimension d: (1) there exists a connected graph with vertex set V that has interference O((log n)^{1/3}); (2) no connected graph with vertex set V has interference o((log n)^{1/4}); and (3) the minimum spanning tree of $V$ has interference Theta((\log n)^{1/2}).
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