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arXiv · 2304.02315

The Laplacian Paradigm in Deterministic Congested Clique

Sebatian Forster·Tijn de Vos
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Abstract

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 $\epsilon$ in $n^{o(1)}\log(1/\epsilon)$ 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 $\tilde{O}(m^{3/7}(n^{0.158}+n^{o(1)}\text{poly}\log W))$ 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 $O(\log n \log^* n)$ rounds, which we believe may be of separate interest.

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Sebatian Forster, Tijn de Vos. 2023-04-05. The Laplacian Paradigm in Deterministic Congested Clique. https://arxiv.org/abs/2304.02315

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