Efficient Enumeration for Conjunctive Queries over X-underbar Structures

Abstract : We investigate efficient enumeration algorithms for conjunctive queries for databases over binary relations that satisfy the X-underbar property. Tree-like relations such as XPath axes or grids are natural examples of such relations. We first show that the result of an n-ary conjunctive query Q over an X-underbar structure S can be enumerated with a delay in O(n.|S|.|Q|) between two consecutive n-tuples. Then, we consider acyclic conjunctive queries and show that such queries admit an enumeration algorithm with delay O(|Q|.|D|) and a preprocessing in O(|Q|.|S|) where D is the domain of S. The delay can even be improved to O(n.|D|) with a slightly more expensive preprocessing step. As an application of our method, we also show that any n-ary XPath acyclic conjunctive query Q over an unranked tree t can be enumerated with a preprocessing and delay O(|Q|.|t|). In the second part of the paper, we consider conjunctive queries with possible inequalities between variables. In this case, we show that query evaluation is NP-hard and, unless P=NP, these queries do not admit enumeration algorithms with a combined polynomial time delay. However, we also show that hardness relies only on the number l of variables that appear in inequalities. We propose efficient enumeration procedures for acyclic and general conjunctive queries whose delay is exponential in l but polynomial (even quasi-linear) in |Q| and |S|.
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Dawar, Anuj and Veith, Helmut. 19th EACSL Annual Conference on Computer Science Logic, Aug 2010, Brno, Czech Republic. Springer, 6247, pp.80-94, 2010, Lecture Notes in computer science. <10.1007/978-3-642-15205-4_10>
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Guillaume Bagan, Arnaud Durand, Emmanuel Filiot, Olivier Gauwin. Efficient Enumeration for Conjunctive Queries over X-underbar Structures. Dawar, Anuj and Veith, Helmut. 19th EACSL Annual Conference on Computer Science Logic, Aug 2010, Brno, Czech Republic. Springer, 6247, pp.80-94, 2010, Lecture Notes in computer science. <10.1007/978-3-642-15205-4_10>. <hal-00489955>

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