Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Direct $\tilde{O}(1/\epsilon)$ Iteration Parallel Algorithm for
  Optimal Transport   Optimal transportation, or computing the Wasserstein or ``earth mover's''
distance between two distributions, is a fundamental primitive which arises in
many learning and statistical settings. We give an algorithm which solves this
problem to additive $\epsilon$ with $\tilde{O}(1/\epsilon)$ parallel depth, and
$\tilde{O}\left(n^2/\epsilon\right)$ work. Barring a breakthrough on a
long-standing algorithmic open problem, this is optimal for first-order
methods. Blanchet et. al. '18, Quanrud '19 obtained similar runtimes through
reductions to positive linear programming and matrix scaling. However, these
reduction-based algorithms use complicated subroutines which may be deemed
impractical due to requiring solvers for second-order iterations (matrix
scaling) or non-parallelizability (positive LP). The fastest practical
algorithms run in time $\tilde{O}(\min(n^2 / \epsilon^2, n^{2.5} / \epsilon))$
(Dvurechensky et. al. '18, Lin et. al. '19). We bridge this gap by providing a
parallel, first-order, $\tilde{O}(1/\epsilon)$ iteration algorithm without
worse dependence on dimension, and provide preliminary experimental evidence
that our algorithm may enjoy improved practical performance. We obtain this
runtime via a primal-dual extragradient method, motivated by recent theoretical
improvements to maximum flow (Sherman '17).

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The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int