Brief Announcement: The Laplacian Paradigm in Deterministic Congested Clique

In this paper, we bring the techniques of the Laplacian paradigm to the congested clique, while further restricting ourselves to deterministic algorithms. In particular, we show how to solve a Laplacian system up to precision is an element of in n(o(1)) log(1/is an element of) rounds. We show how to leverage this result within existing interior point methods for solving flow problems. We obtain an m(3/7+o(1))U(1/7) round algorithm for maximum flow on a weighted directed graph with maximum weight U, and we obtain an (O) over tilde (m(3/7)(n(0.158) + n(o(1)) poly log W)) round algorithm for unit capacity minimum cost flow on a directed graph with maximum cost W. Hereto, we give a novel routine for computing Eulerian orientations in O (logn log*n) rounds, which we believe may be of separate interest.