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arXiv · 1508.04747

Near-Optimal Distributed Maximum Flow

Mohsen Ghaffari·Andreas Karrenbauer·Fabian Kuhn·Christoph Lenzen·Boaz Patt-Shamir
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Abstract

We present a near-optimal distributed algorithm for $(1+o(1))$-approximation of single-commodity maximum flow in undirected weighted networks that runs in $(D+ \sqrt{n})\cdot n^{o(1)}$ communication rounds in the \Congest model. Here, $n$ and $D$ denote the number of nodes and the network diameter, respectively. This is the first improvement over the trivial bound of $O(n^2)$, and it nearly matches the $\tildeΩ(D+ \sqrt{n})$ round complexity lower bound. The development of the algorithm contains two results of independent interest: (i) A $(D+\sqrt{n})\cdot n^{o(1)}$-round distributed construction of a spanning tree of average stretch $n^{o(1)}$. (ii) A $(D+\sqrt{n})\cdot n^{o(1)}$-round distributed construction of an $n^{o(1)}$-congestion approximator consisting of the cuts induced by $O(\log n)$ virtual trees. The distributed representation of the cut approximator allows for evaluation in $(D+\sqrt{n})\cdot n^{o(1)}$ rounds. All our algorithms make use of randomization and succeed with high probability.

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Mohsen Ghaffari, Andreas Karrenbauer, Fabian Kuhn, Christoph Lenzen, Boaz Patt-Shamir. 2015-08-19. Near-Optimal Distributed Maximum Flow. https://arxiv.org/abs/1508.04747

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