Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Target Control of Directed Networks based on Network Flow Problems   Target control of directed networks, which aims to control only a target
subset instead of the entire set of nodes in large natural and technological
networks, is an outstanding challenge faced in various real world applications.
We address one fundamental issue regarding this challenge, i.e., for a given
target subset, how to allocate a minimum number of control sources which
provide input signals to the network nodes. This issue remains open in general
networks with loops. We show that the issue is essentially a path cover problem
and can be further converted into a maximum network flow problem. A method
termed `Maximum Flow based Target Path-cover' (MFTP) with complexity
$O(|V|^{1/2}|E|)$ in which $|V|$ and $|E|$ denote the number of network nodes
and edges is proposed. It is also rigorously proven to provide the minimum
number of control sources on arbitrary directed networks, whether loops exist
or not. We anticipate that this work would serve wide applications in target
control of real-life networks, as well as counter control of various complex
systems which may contribute to enhancing system robustness and resilience.

36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
2
The categories of this paper are: math
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th