Deterministic MST Sparsification in the Congested Clique

Abstract: We give a simple deterministic constant-round algorithm in the congested clique model for reducing the number of edges in a graph to $n^{1+\varepsilon}$ while preserving the minimum spanning forest, where $\varepsilon > 0$ is any constant. This implies that in the congested clique model, it is sufficient to improve MST and other connectivity algorithms on graphs with slightly superlinear number of edges to obtain a general improvement. As a byproduct, we also obtain a simple alternative proof showing that MST can be computed deterministically in $O(\log \log n)$ rounds.