规则2的概率分析
Probabilistic Analysis of Rule 2
摘要：
Li和Wu提出了规则2，一种局部近似算法，试图在图中找到一个小的连通支配集。本文研究了规则2在平面的s_n × s_n正方形区域中由n个随机点构成的随机单位圆盘图上的渐近性质。如果s_n低于连通性阈值，则规则2产生一个支配集，其预期大小为O（n/（loglog n）^{3/2}）。我们推测这个界限不是最优的。
英文摘要：
Li and Wu proposed Rule 2, a localized approximation algorithm that attempts to find a small connected dominating set in a graph. Here we study the asymptotic performance of Rule 2 on random unit disk graphs formed from n random points in an s_n by s_n square region of the plane. If s_n is below the threshold for connectivity, then Rule 2 produces a dominating set whose expected size is O(n/(loglog n)^{3/2}). We conjecture that this bound is not optimal.
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。
