Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computing the atom graph of a graph and the union join graph of a
  hypergraph   The atom graph of a graph is the graph whose vertices are the atoms obtained
by clique minimal separator decomposition of this graph, and whose edges are
the edges of all possible atom trees of this graph. We provide two efficient
algorithms for computing this atom graph, with a complexity in $O(min(n^\alpha
\log n, nm, n(n+\overline{m}))$ time, which is no more than the complexity of
computing the atoms in the general case. %\par We extend our results to
$\alpha$-acyclic hypergraphs. We introduce the notion of union join graph,
which is the union of all possible join trees; we apply our algorithms for atom
graphs to efficiently compute union join graphs.
  Keywords: clique separator decomposition, atom tree, atom graph, clique tree,
clique graph, $\alpha$-acyclic hypergraph.

16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci