We consider geometric problems on planar $n^2$-point sets in the congested clique model. Initially, each node in the $n$-clique network holds a batch of $n$ distinct points in the Euclidean plane given by $O(\log n)$-bit coordinates. In each round, each node can send a distinct $O(\log n)$-bit message to each other node in the clique and perform unlimited local computations. We show that the convex hull of the input $n^2$-point set can be constructed in $O(\min\{ h,\log n\})$ rounds, where $h$ is the size of the hull, on the congested clique. We also show that a triangulation of the input $n^2$-point set can be constructed in $O(\log^2n)$ rounds on the congested clique.

翻译：我们考虑拥塞团簇模型中平面$n^2$点集上的几何问题。初始状态下，$n$节点团簇网络中的每个节点持有由$O(\log n)$位坐标给定的欧几里得平面上的$n$个不同点。每轮通信中，每个节点可向团簇中其他节点发送一条不同的$O(\log n)$位消息，并执行无限制的本地计算。我们证明：在拥塞团簇上，输入$n^2$点集的凸包可在$O(\min\{ h,\log n\})$轮内构建完成，其中$h$为凸包规模。同时表明，输入$n^2$点集的三角剖分可在拥塞团簇上的$O(\log^2 n)$轮内构建完成。