Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Directed Steiner Trees with Multiple Roots   We introduce a new Steiner-type problem for directed graphs named
\textsc{$q$-Root Steiner Tree}. Here one is given a directed graph $G=(V,A)$
and two subsets of its vertices, $R$ of size $q$ and $T$, and the task is to
find a minimum size subgraph of $G$ that contains a path from each vertex of
$R$ to each vertex of $T$. The special case of this problem with $q=1$ is the
well known \textsc{Directed Steiner Tree} problem, while the special case with
$T=R$ is the \textsc{Strongly Connected Steiner Subgraph} problem.
  We first show that the problem is W[1]-hard with respect to $|T|$ for any $q
\ge 2$. Then we restrict ourselves to instances with $R \subseteq T$.
Generalizing the methods of Feldman and Ruhl [SIAM J. Comput. 2006], we present
an algorithm for this restriction with running time $O(2^{2q+4|T|}\cdot
n^{2q+O(1)})$, i.e., this restriction is FPT with respect to $|T|$ for any
constant $q$. We further show that we can, without significantly affecting the
achievable running time, loosen the restriction to only requiring that in the
solution there are a vertex $v$ and a path from each vertex of $R$ to $v$ and
from $v$ to each vertex of~$T$.
  Finally, we use the methods of Chitnis et al. [SODA 2014] to show that the
restricted version can be solved in planar graphs in $O(2^{O(q \log q+|T|\log
q)}\cdot n^{O(\sqrt{q})})$ time.

8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph