Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Structural Tractability of Counting of Solutions to Conjunctive Queries   In this paper we explore the problem of counting solutions to conjunctive
queries. We consider a parameter called the \emph{quantified star size} of a
formula $\varphi$ which measures how the free variables are spread in
$\varphi$. We show that for conjunctive queries that admit nice decomposition
properties (such as being of bounded treewidth or generalized hypertree width)
bounded quantified star size exactly characterizes the classes of queries for
which counting the number of solutions is tractable. This also allows us to
fully characterize the conjunctive queries for which counting the solutions is
tractable in the case of bounded arity. To illustrate the applicability of our
results, we also show that computing the quantified star size of a formula is
possible in time $n^{O(k)}$ for queries of generalized hypertree width $k$.
Furthermore, quantified star size is even fixed parameter tractable
parameterized by some other width measures, while it is $\W{1}$-hard for
generalized hypertree width and thus unlikely to be fixed parameter tractable.
We finally show how to compute an approximation of quantified star size in
polynomial time where the approximation ratio depends on the width of the
input.

22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
2
The categories of this paper are: math
5
The categories of this paper are: gr-qc