Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On solving the densest $k$-subgraph problem on large graphs   The densest $k$-subgraph problem is the problem of finding a $k$-vertex
subgraph of a graph with the maximum number of edges. In order to solve large
instances of the densest $k$-subgraph problem, we introduce two algorithms that
are based on the random coordinate descent approach. Although it is common use
to update at most two random coordinates simultaneously in each iteration of an
algorithm, our algorithms may simultaneously update many coordinates. We show
the benefit of updating more than two coordinates simultaneously for solving
the densest $k$-subgraph problem, and solve large problem instances with up to
$2^{15}$ vertices.

10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg