Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Faster Divergence Maximization for Faster Maximum Flow   In this paper we provide an algorithm which given any $m$-edge $n$-vertex
directed graph with integer capacities at most $U$ computes a maximum $s$-$t$
flow for any vertices $s$ and $t$ in $m^{4/3+o(1)}U^{1/3}$ time. This improves
upon the previous best running times of $m^{11/8+o(1)}U^{1/4}$ (Liu Sidford
2019), $\tilde{O}(m \sqrt{n} \log U)$ (Lee Sidford 2014), and $O(mn)$ (Orlin
2013) when the graph is not too dense or has large capacities.
  To achieve the results this paper we build upon previous algorithmic
approaches to maximum flow based on interior point methods (IPMs). In
particular, we overcome a key bottleneck of previous advances in IPMs for
maxflow (M\k{a}dry 2013, M\k{a}dry 2016, Liu Sidford 2019), which make progress
by maximizing the energy of local $\ell_2$ norm minimizing electric flows. We
generalize this approach and instead maximize the divergence of flows which
minimize the Bregman divergence distance with respect to the weighted
logarithmic barrier. This allows our algorithm to avoid dependencies on the
$\ell_4$ norm that appear in other IPM frameworks (e.g. Cohen M\k{a}dry
Sankowski Vladu 2017, Axiotis M\k{a}dry Vladu 2020). Further, we show that
smoothed $\ell_2$-$\ell_p$ flows (Kyng, Peng, Sachdeva, Wang 2019), which we
previously used to efficiently maximize energy (Liu Sidford 2019), can also be
used to efficiently maximize divergence, thereby yielding our desired runtimes.
We believe both this generalized view of energy maximization and generalized
flow solvers we develop may be of further interest.

6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat