We study the possibility of designing No(1)-round protocols for problems of substantially super-linear polynomial-time (sequential) complexity on the congested clique with about N1/2 nodes, where N is the input size. We show that the average time complexity of the local computation performed at a clique node (in terms of the size of the data received by the node) in such protocols has to be substantially larger than the time complexity of the given problem.
@article{arxiv.2405.15270,
title = {A Note on Solving Problems of Substantially Super-linear Complexity in $N^{o(1)}$ Rounds of the Congested Clique},
author = {Andrzej Lingas},
journal= {arXiv preprint arXiv:2405.15270},
year = {2024}
}