Deterministic MST Sparsification in the Congested Clique

We give a simple deterministic constant-round algorithm in the congested clique model for reducing the number of edges in a graph to n1+ε while preserving the minimum spanning forest, where ε > 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. 1 ar X iv :1 60 5. 02 02 2v 1 [ cs .D C ] 6 M ay 2 01 6