## Conjunctive Queries over Trees (2004)

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Citations: | 67 - 7 self |

### BibTeX

@MISC{Gottlob04conjunctivequeries,

author = {Georg Gottlob and Christoph Koch and Klaus U. Schulz},

title = {Conjunctive Queries over Trees},

year = {2004}

}

### Years of Citing Articles

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### Abstract

We study the complexity and expressive power of conjunctive queries over unranked labeled trees, where the tree structures are represented using "axis relations" such as "child", "descendant", and "following" (we consider a superset of the XPath axes) as well as unary relations for node labels. (Cyclic) conjunctive queries over trees occur in a wide range of data management scenarios related to XML, the Web, and computational linguistics. We establish a framework for characterizing structures representing trees for which conjunctive queries can be evaluated e#- ciently. Then we completely chart the tractability frontier of the problem for our axis relations, i.e., we find all subsetmaximal sets of axes for which query evaluation is in polynomial time. All polynomial-time results are obtained immediately using the proof techniques from our framework. Finally, we study the expressiveness of conjunctive queries over trees and compare it to the expressive power of fragments of XPath. We show that for each conjunctive query, there is an equivalent acyclic positive query (i.e., a set of acyclic conjunctive queries), but that in general this query is not of polynomial size.

### Citations

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Citation Context ... and Nesetril 2004]. Conjunctive queries are surprisingly well-behaved: Many important properties hold for conjunctive queries but fail for more general query languages (cf. [Chandra and Merlin 1977; =-=Abiteboul et al. 1995-=-; Maier 1983]). Unranked labeled trees are a clean abstraction of HTML, XML, LDAP, and linguistic parse trees. This motivates the study of conjunctive queries over trees, where the tree structures are... |

568 |
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Citation Context ...i-muenchen.de), Centrum für Informations- und Sprachverarbeitung, Ludwig-Maximilians-Universität München, D-80536 München, Germany.sthe Constraint Satisfaction problem in AI [Kolaitis and Vardi 1998; =-=Dechter 2003-=-] and the H-coloring problem in graph theory [Hell and Nesetril 2004]. Conjunctive queries are surprisingly well-behaved: Many important properties hold for conjunctive queries but fail for more gener... |

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Citation Context ... Following in P (4.3) Table I. Complexity results for signatures with one or two axes, with pointers to relevant theorems. All NP-hardness results hold already for fixed data trees (query complexity [=-=Vardi 1982-=-]). The polynomial-time upper bounds are established under the assumption that both data and query are variable (combined complexity). —We study the expressive power of conjunctive queries on trees. W... |

498 | Finite Model Theory - Ebbinghaus, Flum - 1999 |

458 |
Optimal Implementation of Conjunctive Queries in Relational Data 8ases
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Citation Context ...lem in graph theory [Hell and Nesetril 2004]. Conjunctive queries are surprisingly well-behaved: Many important properties hold for conjunctive queries but fail for more general query languages (cf. [=-=Chandra and Merlin 1977-=-; Abiteboul et al. 1995; Maier 1983]). Unranked labeled trees are a clean abstraction of HTML, XML, LDAP, and linguistic parse trees. This motivates the study of conjunctive queries over trees, where ... |

435 |
Theory of Relational Databases
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Citation Context ...njunctive queries are surprisingly well-behaved: Many important properties hold for conjunctive queries but fail for more general query languages (cf. [Chandra and Merlin 1977; Abiteboul et al. 1995; =-=Maier 1983-=-]). Unranked labeled trees are a clean abstraction of HTML, XML, LDAP, and linguistic parse trees. This motivates the study of conjunctive queries over trees, where the tree structures are represented... |

411 |
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Citation Context ...ach clause C ∈ C has |C| = 3, is there a truth assignment for U such that each clause in C has exactly one true literal? 1-in-3 3SAT remains NP-complete if all clauses contain only positive literals [=-=Schaefer 1978-=-]. Below, we will use shortcuts of the form χ k (x, y), where χ is an axis, in queries to denote chains of k χ-atoms leading from variable x to y. For example, Child 2 (x, y) is a shortcut for Child(x... |

254 | Efficient algorithms for processing XPath queries
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(Show Context)
Citation Context ...xample, the XPath query //A[B]/following::C is equivalent to the (acyclic) conjunctive query Q(z) ← A(x), Child(x, y), B(y), Following(x, z), C(z). While XPath has been studied extensively (see e.g. [=-=Gottlob et al. 2005-=-; Gottlob et al. 2005] on its complexity, [Benedikt et al. 2003; Olteanu et al. 2002] on its expressive power, and [Hidders 2003] on the satisfiability problem), little work so far has addressed the t... |

216 |
Graphs and Homomorphisms
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Citation Context ...eitung, Ludwig-Maximilians-Universität München, D-80536 München, Germany.sthe Constraint Satisfaction problem in AI [Kolaitis and Vardi 1998; Dechter 2003] and the H-coloring problem in graph theory [=-=Hell and Nesetril 2004-=-]. Conjunctive queries are surprisingly well-behaved: Many important properties hold for conjunctive queries but fail for more general query languages (cf. [Chandra and Merlin 1977; Abiteboul et al. 1... |

196 | Elements of Finite Model Theory - Libkin - 2004 |

179 | Visual web information extraction with lixto - Baumgartner, Flesca, et al. - 2001 |

133 | Conjunctive-query containment and constraint satisfaction
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(Show Context)
Citation Context ... U. Schulz (schulz@cis.uni-muenchen.de), Centrum für Informations- und Sprachverarbeitung, Ludwig-Maximilians-Universität München, D-80536 München, Germany.sthe Constraint Satisfaction problem in AI [=-=Kolaitis and Vardi 1998-=-; Dechter 2003] and the H-coloring problem in graph theory [Hell and Nesetril 2004]. Conjunctive queries are surprisingly well-behaved: Many important properties hold for conjunctive queries but fail ... |

114 | XPath: Looking forward
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- 2002
(Show Context)
Citation Context ...ve query Q(z) ← A(x), Child(x, y), B(y), Following(x, z), C(z). While XPath has been studied extensively (see e.g. [Gottlob et al. 2005; Gottlob et al. 2005] on its complexity, [Benedikt et al. 2003; =-=Olteanu et al. 2002-=-] on its expressive power, and [Hidders 2003] on the satisfiability problem), little work so far has addressed the theoretical properties of cyclic conjunctive queries over trees. Sporadic results on ... |

111 | Algorithms for acyclic database schemes - Yannakakis - 1981 |

105 |
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(Show Context)
Citation Context ...correspond to variables, node labels to unary atoms, and edges to binary atoms). Dominance constraints. Another important issue in computational linguistics are conjunctions of dominance constraints [=-=Marcus et al. 1983-=-], which turn out to be equivalent to (Boolean) conjunctive queries over trees. Dominance constraints 2sS Descendant Descendant NP Following PP Fig. 1. A query graph. have been influential as a means ... |

98 | Conjunctive Query Containment Revisited
- Chekuri, Rajaraman
- 1997
(Show Context)
Citation Context ...sions, if that is possible, and then evaluating them as such may be a practical query evaluation strategy, because there are particularly good algorithms for evaluating such queries [Yannakakis 1981; =-=Chekuri and Rajaraman 1997-=-; Flum et al. 2002; Gottlob and Koch 2004]. We thus study conjunctive queries on tree structures represented using the XPath axis relations child, descendant, descendant-or-self , following-sibling, a... |

90 | Structural properties of XPath fragments
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(Show Context)
Citation Context ...he (acyclic) conjunctive query Q(z) ← A(x), Child(x, y), B(y), Following(x, z), C(z). While XPath has been studied extensively (see e.g. [Gottlob et al. 2005; Gottlob et al. 2005] on its complexity, [=-=Benedikt et al. 2003-=-; Olteanu et al. 2002] on its expressive power, and [Hidders 2003] on the satisfiability problem), little work so far has addressed the theoretical properties of cyclic conjunctive queries over trees.... |

83 | Reformulation of XML Queries and Constraints - Deutsch, Tannen - 2003 |

82 | Query Evaluation via tree decompositions
- Flum, Frick, et al.
(Show Context)
Citation Context ...and then evaluating them as such may be a practical query evaluation strategy, because there are particularly good algorithms for evaluating such queries [Yannakakis 1981; Chekuri and Rajaraman 1997; =-=Flum et al. 2002-=-; Gottlob and Koch 2004]. We thus study conjunctive queries on tree structures represented using the XPath axis relations child, descendant, descendant-or-self , following-sibling, and following. Sinc... |

70 | Monadic Queries over Tree-Structured Data - Gottlob, Koch |

66 | Mars: A system for publishing xml from mixed and redundant storage - Deutsch, Tannen - 2003 |

54 | Duality and polynomial testing of tree homomorphisms
- Hell, Nešeťril, et al.
- 1996
(Show Context)
Citation Context ...course, as mentioned above, there are a number of papers that implicitly contain relevant results [Meuss et al. 2001; Meuss and Schulz 2001; Hidders 2003; Schmidt-Schauß and Stuber 2001]. The papers [=-=Hell et al. 1996-=-a; 1996b] address the complexity of a notion of tree homomorphisms that is uncomparable to the one used in database theory, and the results there are orthogonal. 4 This is equivalent to asking whether... |

40 | The complexity of XPath query evaluation and XML typing
- Gottlob, Koch, et al.
- 2005
(Show Context)
Citation Context ...xample, the XPath query //A[B]/following::C is equivalent to the (acyclic) conjunctive query Q(z) ← A(x), Child(x, y), B(y), Following(x, z), C(z). While XPath has been studied extensively (see e.g. [=-=Gottlob et al. 2005-=-; Gottlob et al. 2005] on its complexity, [Benedikt et al. 2003; Olteanu et al. 2002] on its expressive power, and [Hidders 2003] on the satisfiability problem), little work so far has addressed the t... |

38 |
LTUR: A simplified linear-time unit resolution algorithm for Horn formulae and computer implementation
- Minoux
- 1988
(Show Context)
Citation Context ...ed by Θ(x) ↦→ {v | (x, v) ∈ T }, for each x, is obviously arc-consistent and contains all arc-consistent pre-valuations of Q and A. Program P can be computed and solved (e.g. using Minoux’ algorithm [=-=Minoux 1988-=-]), and the solution complemented, in time linear in the size of the program, which is O(||A|| · |Q|). ✷ Actually, this algorithm computes the unique subset-maximal arc-consistent prevaluation of Q on... |

36 | Order Paths in Ordered Trees
- “First
(Show Context)
Citation Context ... be formulated as an XPath query. This is in contrast to full first-order logic (i.e., with negation) on trees, which is known to be stronger than acyclic first-order logic on trees resp. Core XPath [=-=Marx 2005-=-]. Obviously, the CQ[F] are not closed under union. On trees of one node only, conjunctive queries are equivalent to ones which do not use binary atoms. It is easy to see that the query {x | A(x) ∨ B(... |

34 | Satisfiability of XPath Expressions - Hidders - 2003 |

27 |
On the exponent of periodicity of minimal solutions of context equation. volume 1379
- Schmidt-Schauß, Schulz
- 1998
(Show Context)
Citation Context ...order unification. The query evaluation problem for conjunctive queries over trees is also closely related to the context matching problem 1 , a variant of the well-known context-unification problem [=-=Schmidt-Schauß and Schulz 1998-=-; 2002]. Some tractability frontier for the context matching problem is outlined in [SchmidtSchauß and Stuber 2001]. However, little insight is gained from this for the database context, since the cla... |

25 | Monadic datalog and the Expressive Power of Web Information Extraction Languages - Gottlob, Koch - 2004 |

25 | Solvability of context equations with two context variables is decidable - Schmidt-Schauß, Schulz |

21 |
Finite Model Theory, Springer-Verlag
- Ebbinghaus, Flum
- 1995
(Show Context)
Citation Context ...s. For a relational structure A, let A = |A| denote the finite domain (in the case of a tree, the nodes) and let ||A|| denote the size of the structure under any reasonable encoding scheme (see e.g. [=-=Ebbinghaus and Flum 1999-=-]). We use the binary axis relations Child (defined in the normal way) and NextSibling (where NextSibling(v, w) if and only if w is the right neighboring 5ssibling of v in the tree), their transitive ... |

21 | Complete Answer Aggregates for Treelike Databases: a novel Approach to combine querying and navigation
- Meuss, Schulz
- 2001
(Show Context)
Citation Context ...le work so far has addressed the theoretical properties of cyclic conjunctive queries over trees. Sporadic results on their complexity can be found in [Meuss et al. 2001; Gottlob and Koch 2002; 2004; =-=Meuss and Schulz 2001-=-]. Data extraction and integration. (Cyclic) conjunctive queries on trees have been used previously in data integration, where queries in languages such as XQuery were canonically mapped to conjunctiv... |

21 | On diving in trees - Schwentick |

17 |
Complexity of tree homomorphisms
- Hell, Neˇsetˇril, et al.
- 1996
(Show Context)
Citation Context ...course, as mentioned above, there are a number of papers that implicitly contain relevant results [Meuss et al. 2001; Meuss and Schulz 2001; Hidders 2003; Schmidt-Schauß and Stuber 2001]. The papers [=-=Hell et al. 1996-=-a; 1996b] address the complexity of a notion of tree homomorphisms that is uncomparable to the one used in database theory, and the results there are orthogonal. 4 This is equivalent to asking whether... |

16 | Towards Aggregated Answers for Semistructured Data
- Meuss, Schulz, et al.
- 2001
(Show Context)
Citation Context ...dders 2003] on the satisfiability problem), little work so far has addressed the theoretical properties of cyclic conjunctive queries over trees. Sporadic results on their complexity can be found in [=-=Meuss et al. 2001-=-; Gottlob and Koch 2002; 2004; Meuss and Schulz 2001]. Data extraction and integration. (Cyclic) conjunctive queries on trees have been used previously in data integration, where queries in languages ... |

15 | On the Complexity of Linear and Stratified Context Matching Problems”. Unpublished manuscript - Schmidt-Schauß, Stuber |

14 | A New Algorithm for Normal Dominance Constraints
- Bodirsky, Duchier, et al.
- 2004
(Show Context)
Citation Context ...ing and disambiguation remain ambiguous. One problem of practical importance is the rewriting of sets of dominance constraints into equivalent but simpler sets (in particular, so-called solved forms [=-=Bodirsky et al. 2004-=-], which correspond to acyclic queries). This implies that studying the expressive power of conjunctive queries over trees, and the problem of deciding whether there is a set of acyclic conjunctive qu... |

10 | Symmetry in XPath - Olteanu, Meuss, et al. |

9 | The complexity of XPath query processing - Jarke, Koch, et al. - 2003 |

1 |
The Penn Treebank Project”. http://www.cis.upenn.edu/∼treebank/home.html
- LDC
- 1999
(Show Context)
Citation Context ...er area in which such queries are employed is computational linguistics, where one needs to search in, or check properties of, large corpora of parsed natural language. Corpora such as Penn Treebank [=-=LDC 1999-=-] are unranked trees labeled with the phrase structure of parsed (for Treebank, financial news) text. A query asking for prepositional phrases following noun phrases in the same sentence can be phrase... |

1 | The Penn Treebank Project - LDC - 1999 |

1 |
Optimal Implementation of Conjunctive Queries 34 Relational Data Bases
- Chandra, Merlin
- 1977
(Show Context)
Citation Context ...lem in graph theory [Hell and Nesetril 2004]. Conjunctive queries are surprisingly well-behaved: Many important properties hold for conjunctive queries but fail for more general query languages (cf. [=-=Chandra and Merlin 1977-=-; Abiteboul et al. 1995; Maier 1983]). Unranked labeled trees are a clean abstraction of HTML, XML, LDAP, and linguistic parse trees. This motivates the study of conjunctive queries over trees, where ... |