In this short paper, we present an improved algorithm for approximating the
minimum cut on distributed (CONGEST) networks. Let λ be the minimum
cut. Our algorithm can compute λ 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 O~ hides
\poly\log n. By a standard reduction, we can convert this algorithm into a
(1+ϵ)-approximation \tilde{O}((\sqrt{n}+D)/\poly(\epsilon))-time
algorithm. The latter result improves over the previous
(2+ϵ)-approximation \tilde{O}((\sqrt{n}+D)/\poly(\epsilon))-time
algorithm of Ghaffari and Kuhn [DISC 2013]. Due to the lower bound of
Ω~(n+D) by Das Sarma et al. [SICOMP 2013], this running
time is {\em tight} up to a \poly\log n factor. Our algorithm is an extremely
simple combination of Thorup's tree packing theorem [Combinatorica 2007],
Kutten and Peleg's tree partitioning algorithm [J. Algorithms 1998], and
Karger's dynamic programming [JACM 2000].Comment: To appear as a brief announcement at PODC 201