Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fast Algorithms for Computational Optimal Transport and Wasserstein
  Barycenter   We provide theoretical complexity analysis for new algorithms to compute the
optimal transport (OT) distance between two discrete probability distributions,
and demonstrate their favorable practical performance over state-of-art
primal-dual algorithms and their capability in solving other problems in
large-scale, such as the Wasserstein barycenter problem for multiple
probability distributions. First, we introduce the \emph{accelerated
primal-dual randomized coordinate descent} (APDRCD) algorithm for computing the
OT distance. We provide its complexity upper bound
$\bigOtil(\frac{n^{5/2}}{\varepsilon})$ where $n$ stands for the number of
atoms of these probability measures and $\varepsilon > 0$ is the desired
accuracy. This complexity bound matches the best known complexities of
primal-dual algorithms for the OT problems, including the adaptive primal-dual
accelerated gradient descent (APDAGD) and the adaptive primal-dual accelerated
mirror descent (APDAMD) algorithms. Then, we demonstrate the better performance
of the APDRCD algorithm over the APDAGD and APDAMD algorithms through extensive
experimental studies, and further improve its practical performance by
proposing a greedy version of it, which we refer to as \emph{accelerated
primal-dual greedy coordinate descent} (APDGCD). Finally, we generalize the
APDRCD and APDGCD algorithms to distributed algorithms for computing the
Wasserstein barycenter for multiple probability distributions.

21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin