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34
Taming the infinite chase: Query answering under expressive relational constraints
 In Proc. of KR 2008
, 2008
"... The chase algorithm is a fundamental tool for query evaluation and for testing query containment under tuplegenerating dependencies (TGDs) and equalitygenerating dependencies (EGDs). So far, most of the research on this topic has focused on cases where the chase procedure terminates. This paper in ..."
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Cited by 56 (13 self)
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The chase algorithm is a fundamental tool for query evaluation and for testing query containment under tuplegenerating dependencies (TGDs) and equalitygenerating dependencies (EGDs). So far, most of the research on this topic has focused on cases where the chase procedure terminates. This paper introduces expressive classes of TGDs defined via syntactic restrictions: guarded TGDs (GTGDs) and weakly guarded sets of TGDs (WGTGDs). For these classes, the chase procedure is not guaranteed to terminate and thus may have an infinite outcome. Nevertheless, we prove that the problems of conjunctivequery answering and query containment under such TGDs are decidable. We provide decision procedures and tight complexity bounds for these problems. Then we show how EGDs can be incorporated into our results by providing conditions under which EGDs do not harmfully interact with TGDs and do not affect the decidability and complexity of query answering. We show applications of the aforesaid classes of constraints to the problem of answering conjunctive queries in FLogic Lite, an objectoriented ontology language, and in some tractable Description Logics. 1.
A unified theory of structural tractability for constraint satisfaction and spread cut decomposition
 In Proceedings of the 19th International Joint Conference on Artificial Intelligence
, 2005
"... In this paper we introduce a generic form of structural decomposition for the constraint satisfaction problem, which we call a guarded decomposition. We show that many existing decomposition methods can be characterized in terms of finding guarded decompositions satisfying certain specified addition ..."
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Cited by 22 (2 self)
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In this paper we introduce a generic form of structural decomposition for the constraint satisfaction problem, which we call a guarded decomposition. We show that many existing decomposition methods can be characterized in terms of finding guarded decompositions satisfying certain specified additional conditions. Using the guarded decomposition framework we are also able to define a new form of decomposition, which we call a spread cut. We show that discovery of width k spreadcut decompositions is tractable for each k, and that the spread cut decomposition strongly generalize all existing decompositions except hypertrees. Finally we exhibit a family of hypergraphs Hn, for n = 1, 2, 3..., where the width of the best hypertree decomposition of each Hn is at least 3n, but the width of the best spreadcut decomposition is at most 2n. 1
On querying simple conceptual graphs with negation
 IN: DATA AND KNOWLEDGE ENGINEERING, DKE, ELSEVIER, REVISED VERSION OF R.R. LIRMM
, 2006
"... We consider basic conceptual graphs, namely simple conceptual graphs (SGs), which are equivalent to the existential conjunctive positive fragment of firstorder logic. The fundamental problem, deduction, is performed by a graph homomorphism called projection. The existence of a projection from a SG ..."
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Cited by 10 (6 self)
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We consider basic conceptual graphs, namely simple conceptual graphs (SGs), which are equivalent to the existential conjunctive positive fragment of firstorder logic. The fundamental problem, deduction, is performed by a graph homomorphism called projection. The existence of a projection from a SG Q to a SG G means that the knowledge represented by Q is deducible from the knowledge represented by G. In this framework, a knowledge base is composed of SGs representing facts and a query is itself a SG. We focus on the issue of querying SGs, which highlights another fundamental problem, namely query answering. Each projection from a query to a fact defines an answer to the query, with an answer being itself a SG. The query answering problem asks for all answers to a query. This paper introduces atomic negation into this framework. Several understandings of negation are explored, which are all of interest in real world applications. In particular, we focus on situations where, in the context of incomplete knowledge, classical negation is not satisfactory because deduction can be proven but there is no answer to the query. We show that intuitionistic deduction captures the notion of an answer and can be solved by projection checking. Algorithms are provided for all studied problems. They are all based on projection. They can thus be combined to deal with several kinds of negation simultaneously. Relationships with problems on conjunctive queries in databases are recalled and extended. Finally, we point out that this discussion can be put in the context of semantic web databases.
Constraint satisfaction with bounded treewidth revisited
 In CP’06
, 2006
"... We consider the constraint satisfaction problem (CSP) parameterized by the treewidth of primal, dual, and incidence graphs, combined with several other basic parameters such as domain size and arity. We determine all combinations of the considered parameters that admit fixedparameter tractability. ..."
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Cited by 10 (2 self)
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We consider the constraint satisfaction problem (CSP) parameterized by the treewidth of primal, dual, and incidence graphs, combined with several other basic parameters such as domain size and arity. We determine all combinations of the considered parameters that admit fixedparameter tractability. Key words: Constraint satisfaction, parameterized complexity, treewidth 1
Weighted hypertree decompositions and optimal query plans
 In Proc. of PODS’04
, 2004
"... Hypertree width [22, 25] is a measure of the degree of cyclicity of hypergraphs. A number of relevant problems from different areas, e.g., the evaluation of conjunctive queries in database theory or the constraint satisfaction in AI, are tractable when their underlying hypergraphs have bounded hyper ..."
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Cited by 9 (2 self)
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Hypertree width [22, 25] is a measure of the degree of cyclicity of hypergraphs. A number of relevant problems from different areas, e.g., the evaluation of conjunctive queries in database theory or the constraint satisfaction in AI, are tractable when their underlying hypergraphs have bounded hypertree width. However, in practical contexts like the evaluation of database queries, we have more information besides the structure of queries. For instance, we know the number of tuples in relations, the selectivity of attributes and so on. In fact, all commercial queryoptimizers are based on quantitative methods and do not care about structural properties. In this paper, we define the notion of weighted hypertree decomposition, in order to combine structural decomposition methods with quantitative approaches. Weighted hypertree decompositions are equipped with cost functions, that can be used for modelling many
Exact algorithms and applications for Treelike Weighted Set Cover
 JOURNAL OF DISCRETE ALGORITHMS
, 2006
"... We introduce an NPcomplete special case of the Weighted Set Cover problem and show its fixedparameter tractability with respect to the maximum subset size, a parameter that appears to be small in relevant applications. More precisely, in this practically relevant variant we require that the given ..."
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Cited by 9 (4 self)
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We introduce an NPcomplete special case of the Weighted Set Cover problem and show its fixedparameter tractability with respect to the maximum subset size, a parameter that appears to be small in relevant applications. More precisely, in this practically relevant variant we require that the given collection C of subsets of a some base set S should be “treelike.” That is, the subsets in C can be organized in a tree T such that every subset onetoone corresponds to a tree node and, for each element s of S, the nodes corresponding to the subsets containing s induce a subtree of T. This is equivalent to the problem of finding a minimum edge cover in an edgeweighted acyclic hypergraph. Our main result is an algorithm running in O(3 k ·mn) time where k denotes the maximum subset size, n: = S, and m: = C. The algorithm also implies a fixedparameter tractability result for the NPcomplete Multicut in Trees problem, complementing previous approximation results. Our results find applications in computational biology in phylogenomics and for saving memory in tree decomposition based graph algorithms.
Grounding for model expansion in kguarded formulas with inductive definitions
 In IJCAI
, 2007
"... Mitchell and Ternovska [2005] proposed a constraint programming framework based on classical logic extended with inductive definitions. They formulate a search problem as the problem of model expansion (MX), which is the problem of expanding a given structure with new relations so that it satisfies ..."
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Cited by 8 (4 self)
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Mitchell and Ternovska [2005] proposed a constraint programming framework based on classical logic extended with inductive definitions. They formulate a search problem as the problem of model expansion (MX), which is the problem of expanding a given structure with new relations so that it satisfies a given formula. Their longterm goal is to produce practical tools to solve combinatorial search problems, especially those in NP. In this framework, a problem is encoded in a logic, an instance of the problem is represented by a finite structure, and a solver generates solutions to the problem. This approach relies on propositionalisation of highlevel specifications, and on the efficiency of modern SAT solvers. Here, we propose an efficient algorithm which combines grounding with partial evaluation. Since the MX framework is based on classical logic, we are able to take advantage of known results for the socalled guarded fragments. In the case of kguarded formulas with inductive definitions under a natural restriction, the algorithm performs much better than naive grounding by relying on connections between kguarded formulas and tree decompositions. 1
A combinatorial approach to conceptual graph projection checking
 In Proc. of the 24th Int’l Conf. of the Brit. Comp. Society’s Spec. Group on Artif. Intell. (AI’2004
, 2004
"... We exploit the combinatorial structure of conceptual graphs in order to obtain better execution times when computing projection, which is a core generalisationspecialisation relation over conceptual graphs. We show how the problem of finding this relation can be translated into the Maximum Clique p ..."
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Cited by 7 (4 self)
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We exploit the combinatorial structure of conceptual graphs in order to obtain better execution times when computing projection, which is a core generalisationspecialisation relation over conceptual graphs. We show how the problem of finding this relation can be translated into the Maximum Clique problem. Consequently, approximation techniques developed for the Maximum Clique problem can be used to compute projection in conceptual graphs. We show that there are “simple queries” which can be answered quickly, thus providing efficient reasoning support in a knowledge management environment based on conceptual graphs. 1
Undirected graphs of entanglement 2
, 2007
"... Abstract. Entanglement is a complexity measure of directed graphs that origins in fixed point theory. This measure has shown its use in designing efficient algorithms to verify logical properties of transition systems. We are interested in the problem of deciding whether a graph has entanglement at ..."
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Cited by 4 (2 self)
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Abstract. Entanglement is a complexity measure of directed graphs that origins in fixed point theory. This measure has shown its use in designing efficient algorithms to verify logical properties of transition systems. We are interested in the problem of deciding whether a graph has entanglement at most k. As this measure is defined by means of games, game theoretic ideas naturally lead to design polynomial algorithms that, for fixed k, decide the problem. Known characterizations of directed graphs of entanglement at most 1 lead, for k = 1, to design even faster algorithms. In this paper we give two distinct characterizations of undirected graphs of entanglement at most 2. With these characterizations at hand, we present a linear time algorithm to decide whether an undirected graph has this property. 1
A tree decomposition algorithm for Conceptual Graph projection
"... This paper discusses combinatorial mechanisms for reasoning with conceptual graphs. We focus on the combinatorial aspects of a backtracking approach to the NPhard problem of projection, which is the main tool for reasoning with conceptual graphs. We use effective graphtheoretical lookahead proced ..."
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Cited by 3 (2 self)
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This paper discusses combinatorial mechanisms for reasoning with conceptual graphs. We focus on the combinatorial aspects of a backtracking approach to the NPhard problem of projection, which is the main tool for reasoning with conceptual graphs. We use effective graphtheoretical lookahead procedures, based on a conceptual forest decomposition of the graph to be projected. We believe that our approach to projection can improve the practical applicability of exponential algorithms currently used to solve NPhard problems. 1