Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Information Flow Problem on Clock Networks   The information flow problem on a network asks whether $r$ senders, $v_1,v_2,
\ldots ,v_r$ can each send messages to $r$ corresponding receivers $v_{n+1},
\ldots ,v_{n+r}$ via intermediate nodes $v_{r+1}, \ldots ,v_n$. For a given
finite $R \subset \mathbb{Z}^+$, the clock network $N_n(R)$ has edge $v_iv_k$
if and only if $k>r$ and $k-i \in R$. We show that the information flow problem
on $N_n(\{1,2, \ldots ,r\})$ can be solved for all $n \geq r$. We also show
that for any finite $R$ such that $\gcd(R)=1$ and $r = \max(R)$, we show that
the information flow problem can be solved on $N_n(R)$ for all $n \geq 3r^3$.

29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga