Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A scalable distributed dynamical systems approach to compute the
  strongly connected components and diameter of networks   Finding strongly connected components (SCCs) and the diameter of a directed
network play a key role in a variety of discrete optimization problems, and
subsequently, machine learning and control theory problems. On the one hand,
SCCs are used in solving the 2-satisfiability problem, which has applications
in clustering, scheduling, and visualization. On the other hand, the diameter
has applications in network learning and discovery problems enabling efficient
internet routing and searches, as well as identifying faults in the power grid.
  In this paper, we leverage consensus-based principles to find the SCCs in a
scalable and distributed fashion with a computational complexity of
$\mathcal{O}\left(Dd_{\text{in-degree}}^{\max}\right)$, where $D$ is the
(finite) diameter of the network and $d_{\text{in-degree}}^{\max}$ is the
maximum in-degree of the network. Additionally, we prove that our algorithm
terminates in $D+1$ iterations, which allows us to retrieve the diameter of the
network. We illustrate the performance of our algorithm on several random
networks, including Erd\H{o}s-R\'enyi, Barab\'asi-Albert, and
\mbox{Watts-Strogatz} networks.

22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph