Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Minimum Wiener Connector   The Wiener index of a graph is the sum of all pairwise shortest-path
distances between its vertices. In this paper we study the novel problem of
finding a minimum Wiener connector: given a connected graph $G=(V,E)$ and a set
$Q\subseteq V$ of query vertices, find a subgraph of $G$ that connects all
query vertices and has minimum Wiener index.
  We show that The Minimum Wiener Connector admits a polynomial-time (albeit
impractical) exact algorithm for the special case where the number of query
vertices is bounded. We show that in general the problem is NP-hard, and has no
PTAS unless $\mathbf{P} = \mathbf{NP}$. Our main contribution is a
constant-factor approximation algorithm running in time
$\widetilde{O}(|Q||E|)$.
  A thorough experimentation on a large variety of real-world graphs confirms
that our method returns smaller and denser solutions than other methods, and
does so by adding to the query set $Q$ a small number of important vertices
(i.e., vertices with high centrality).

3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th