We study the possibility of designing $N^{o(1)}$-round protocols for problems of substantially super-linear polynomial-time complexity on the congested clique with about $N^{1/2}$ nodes, where $N$ is the input size. We show that the exponent of the polynomial (if any) bounding the average time complexity of local computations performed at a node in such protocols has to be larger than that of the polynomial bounding the time complexity of the given problem.

翻译：我们研究了在节点数约为$N^{1/2}$的拥塞团模型中，为具有实质超线性多项式时间复杂度的问题设计$N^{o(1)}$轮协议的可能性。我们证明，在此类协议中，节点本地计算的平均时间复杂度所对应的多项式指数（若存在），必须大于给定问题时间复杂度所对应的多项式指数。