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Article overview
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Structural Tractability of Counting of Solutions to Conjunctive Queries | | Arnaud Durand
; Stefan Mengel
; | | Date: |
8 Mar 2013 | | Abstract: | 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. | | Source: | arXiv, 1303.2059 | | Services: | Forum | Review | PDF | Favorites | |
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