The relationship between apsp and matrix multiplication in congested clique

This month, the Distributed Computing Column is featuring Dean Leitersdorf, Award. His work on sparse matrix multiplication has led to several breakthroughs that improve significantly on the state of the art. These new approaches have led to faster algorithms for a variety of related problems, including constant-round algorithms for computing graph spanners, approximate all-pairs-shortest-paths, and the girth of a graph (up to an additive 1) in the congested clique model. Recent progress in distributed matrix multiplication has been fast, and realworld applications of matrix multiplication have only been increasing in importance. In this column, Dean Leitersdorf gives an overview of the state of the art for distributed matrix multiplication, and its connection to all-pairs shortest paths in the congested clique model. He provides both a summary of his new sparityaware approach, along with a discussion of open questions and possible future directions. Overall, then, this column provides a succinct overview of a rapidly moving area of distributed algorithms!