Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A heuristic use of dynamic programming to upperbound treewidth   For a graph $G$, let $\Pi(G)$ denote the set of all potential maximal cliques
of $G$. For each subset $\Pi$ of $\Pi(G)$, let $\tw(G, \Pi)$ denote the
smallest $k$ such that there is a tree-decomposition of $G$ of width $k$ whose
bags all belong to $\Pi$. Bouchitt\'{e} and Todinca observed in 2001 that
$\tw(G, \Pi(G))$ is exactly the treewidth of $G$ and developed a dynamic
programming algorithm to compute it. Indeed, their algorithm can readily be
applied to an arbitrary non-empty subset $\Pi$ of $\Pi(G)$ and computes $\tw(G,
\Pi)$, or reports that it is undefined, in time $|\Pi||V(G)|^{O(1)}$. This
efficient tool for computing $\tw(G, \Pi)$ allows us to conceive of an
iterative improvement procedure for treewidth upper bounds which maintains, as
the current solution, a set of potential maximal cliques rather than a
tree-decomposition.
  We design and implement an algorithm along this approach. Experiments show
that our algorithm vastly outperforms previously implemented heuristic
algorithms for treewidth.

18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat