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In this short paper, we present an improved algorithm for approximating theminimum cut on distributed (CONGEST) networks. Let $\lambda$ be the minimumcut. Our algorithm can compute $\lambda$ exactly in$\tilde{O}((\sqrt{n}+D)\poly(\lambda))$ time, where $n$ is the number of nodes(processors) in the network, $D$ is the network diameter, and $\tilde{O}$ hides$\poly\log n$. By a standard reduction, we can convert this algorithm into a$(1+\epsilon)$-approximation $\tilde{O}((\sqrt{n}+D)/\poly(\epsilon))$-timealgorithm. The latter result improves over the previous$(2+\epsilon)$-approximation $\tilde{O}((\sqrt{n}+D)/\poly(\epsilon))$-timealgorithm of Ghaffari and Kuhn [DISC 2013]. Due to the lower bound of$\tilde{\Omega}(\sqrt{n}+D)$ by Das Sarma et al. [SICOMP 2013], this runningtime is {\em tight} up to a $\poly\log n$ factor. Our algorithm is an extremelysimple combination of Thorup's tree packing theorem [Combinatorica 2007],Kutten and Peleg's tree partitioning algorithm [J. Algorithms 1998], andKarger's dynamic programming [JACM 2000].

Brief Announcement: Almost-Tight Approximation Distributed Algorithm for Minimum Cut