Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximum Flow and Minimum-Cost Flow in Almost-Linear Time   We give an algorithm that computes exact maximum flows and minimum-cost flows
on directed graphs with $m$ edges and polynomially bounded integral demands,
costs, and capacities in $m^{1+o(1)}$ time. Our algorithm builds the flow
through a sequence of $m^{1+o(1)}$ approximate undirected minimum-ratio cycles,
each of which is computed and processed in amortized $m^{o(1)}$ time using a
new dynamic graph data structure.
  Our framework extends to algorithms running in $m^{1+o(1)}$ time for
computing flows that minimize general edge-separable convex functions to high
accuracy. This gives almost-linear time algorithms for several problems
including entropy-regularized optimal transport, matrix scaling, $p$-norm
flows, and $p$-norm isotonic regression on arbitrary directed acyclic graphs.

12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin