We give a simple, local process for nodes in an undirected graph to form non-adjacent clusters that (1) have at most a polylogarithmic diameter and (2) contain at least half of all vertices. Efficient deterministic distributed clustering algorithms for computing strong-diameter network decompositions and other key tools follow immediately. Overall, our process is a direct and drastically simplified way for computing these fundamental objects.

翻译：我们给无方向图中的节点提供一个简单、局部的过程,以形成非相邻的群集,这些群集:(1) 最多具有多元直径,(2) 包含至少所有脊椎的一半。 计算强直径网络分解和其他关键工具的高效的确定性分布式群集算法随之而来。 总体而言,我们的过程是直接和大幅度简化的计算这些基本物体的方法。