Results 1  10
of
101
A comparison of structural CSP decomposition methods
 Artificial Intelligence
, 2000
"... We compare tractable classes of constraint satisfaction problems (CSPs). We first give a uniform presentation of the major structural CSP decomposition methods. We then introduce a new class of tractable CSPs based on the concept of hypertree decomposition recently developed in Database Theory. We i ..."
Abstract

Cited by 149 (17 self)
 Add to MetaCart
We compare tractable classes of constraint satisfaction problems (CSPs). We first give a uniform presentation of the major structural CSP decomposition methods. We then introduce a new class of tractable CSPs based on the concept of hypertree decomposition recently developed in Database Theory. We introduce a framework for comparing parametric decompositionbased methods according to tractability criteria and compare the most relevant methods. We show that the method of hypertree decomposition dominates the others in the case of general (nonbinary) CSPs.
ConjunctiveQuery Containment and Constraint Satisfaction
 Journal of Computer and System Sciences
, 1998
"... Conjunctivequery containment is recognized as a fundamental problem in database query evaluation and optimization. At the same time, constraint satisfaction is recognized as a fundamental problem in artificial intelligence. What do conjunctivequery containment and constraint satisfaction have in c ..."
Abstract

Cited by 132 (13 self)
 Add to MetaCart
Conjunctivequery containment is recognized as a fundamental problem in database query evaluation and optimization. At the same time, constraint satisfaction is recognized as a fundamental problem in artificial intelligence. What do conjunctivequery containment and constraint satisfaction have in common? Our main conceptual contribution in this paper is to point out that, despite their very different formulation, conjunctivequery containment and constraint satisfaction are essentially the same problem. The reason is that they can be recast as the following fundamental algebraic problem: given two finite relational structures A and B, is there a homomorphism h : A ! B? As formulated above, the homomorphism problem is uniform in the sense that both relational structures A and B are part of the input. By fixing the structure B, one obtains the following nonuniform problem: given a finite relational structure A, is there a homomorphism h : A ! B? In general, nonuniform tractability results do not uniformize. Thus, it is natural to ask: which tractable cases of nonuniform tractability results for constraint satisfaction and conjunctivequery containment do uniformize? Our main technical contribution in this paper is to show that several cases of tractable nonuniform constraint satisfaction problems do indeed uniformize. We exhibit three nonuniform tractability results that uniformize and, thus, give rise to polynomialtime solvable cases of constraint satisfaction and conjunctivequery containment.
Pure Nash Equilibria: Hard and Easy Games
"... In this paper we investigate complexity issues related to pure Nash equilibria of strategic games. We show that, even in very restrictive settings, determining whether a game has a pure Nash Equilibrium is NPhard, while deciding whether a game has a strong Nash equilibrium is Stcomplete. We then s ..."
Abstract

Cited by 63 (2 self)
 Add to MetaCart
In this paper we investigate complexity issues related to pure Nash equilibria of strategic games. We show that, even in very restrictive settings, determining whether a game has a pure Nash Equilibrium is NPhard, while deciding whether a game has a strong Nash equilibrium is Stcomplete. We then study practically relevant restrictions that lower the complexity. In particular, we are interested in quantitative and qualitative restrictions of the way each player's move depends on moves of other players. We say that a game has small neighborhood if the " utility function for each player depends only on (the actions of) a logarithmically small number of other players, The dependency structure of a game G can he expressed by a graph G(G) or by a hypergraph II(G). Among other results, we show that if jC has small neighborhood and if II(G) has botmdecl hypertree width (or if G(G) has bounded treewidth), then finding pure Nash and Pareto equilibria is feasible in polynomial time. If the game is graphical, then these problems are LOGCFLcomplete and thus in the class _NC ~ of highly parallelizable problems. 1 Introduction and Overview of Results The theory of strategic games and Nash equilibria has important applications in economics and decision making [31, 2]. Determining whether Nash equilibria exist, and effectively computing
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 ..."
Abstract

Cited by 51 (12 self)
 Add to MetaCart
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.
New Results on Monotone Dualization and Generating Hypergraph Transversals
 SIAM JOURNAL ON COMPUTING
, 2002
"... We consider the problem of dualizing a monotone CNF (equivalently, computing all minimal transversals of a hypergraph), whose associated decision problem is a prominent open problem in NPcompleteness. We present a number of new polynomial time resp. outputpolynomial time results for significant ..."
Abstract

Cited by 37 (12 self)
 Add to MetaCart
We consider the problem of dualizing a monotone CNF (equivalently, computing all minimal transversals of a hypergraph), whose associated decision problem is a prominent open problem in NPcompleteness. We present a number of new polynomial time resp. outputpolynomial time results for significant cases, which largely advance the tractability frontier and improve on previous results. Furthermore, we show that duality of two monotone CNFs can be disproved with limited nondeterminism. More precisely, this is feasible in polynomial time with O(log² n/log log n) suitably guessed bits. This result sheds new light on the complexity of this important problem.
Xpath leashed
 IN ACM COMPUTING SURVEYS
, 2007
"... This survey gives an overview of formal results on the XML query language XPath. We identify several important fragments of XPath, focusing on subsets of XPath 1.0. We then give results on the expressiveness of XPath and its fragments compared to other formalisms for querying trees, algorithms and c ..."
Abstract

Cited by 36 (3 self)
 Add to MetaCart
This survey gives an overview of formal results on the XML query language XPath. We identify several important fragments of XPath, focusing on subsets of XPath 1.0. We then give results on the expressiveness of XPath and its fragments compared to other formalisms for querying trees, algorithms and complexity bounds for evaluation of XPath queries, and static analysis of XPath queries.
Querying the web reconsidered: Design principles for versatile web query languages
 Journal of Semantic Web and Information Systems
, 2005
"... A decade of experience with research proposals as well as standardized query languages for the conventional Web and the recent emergence of query languages for the Semantic Web call for a reconsideration of design principles for Web and Semantic Web query languages. This article first argues that a ..."
Abstract

Cited by 31 (19 self)
 Add to MetaCart
A decade of experience with research proposals as well as standardized query languages for the conventional Web and the recent emergence of query languages for the Semantic Web call for a reconsideration of design principles for Web and Semantic Web query languages. This article first argues that a new generation of versatile Web query languages is needed for solving the challenges posed by the changing Web: We call versatile those query languages able to cope with both Web and Semantic Web data expressed in any (Web or Semantic Web) markup language. This article further suggests that (wellknown) referential transparency and (novel) answerclosedness are essential features of versatile query languages. Indeed, they allow queries to be considered like forms and answers like formfillings in the spirit of the “querybyexample ” paradigm. This article finally suggests that the decentralized and heterogeneous nature of the Web requires incomplete data specifications (or “incomplete queries”) and incomplete data selections (or “incomplete answers”): the formlike query can be specified without precise knowledge of the queried data and answers can be restricted to contain only an excerpt of the queried data. 1.
Fixedparameter tractability, definability, and model checking
 SIAM Journal on Computing
, 2001
"... In this article, we study parameterized complexity theory from the perspective of logic, or more specifically, descriptive complexity theory. We propose to consider parameterized modelchecking problems for various fragments of firstorder logic as generic parameterized problems and show how this ap ..."
Abstract

Cited by 30 (12 self)
 Add to MetaCart
In this article, we study parameterized complexity theory from the perspective of logic, or more specifically, descriptive complexity theory. We propose to consider parameterized modelchecking problems for various fragments of firstorder logic as generic parameterized problems and show how this approach can be useful in studying both fixedparameter tractability and intractability. For example, we establish the equivalence between the modelchecking for existential firstorder logic, the homomorphism problem for relational structures, and the substructure isomorphism problem. Our main tractability result shows that modelchecking for firstorder formulas is fixedparameter tractable when restricted to a class of input structures with an excluded minor. On the intractability side, for everyØ�we prove an equivalence between modelchecking for firstorder formulas withØquantifier alternations and the parameterized halting problem for alternating Turing machines withØalternations. We discuss the close connection between this alternation hierarchy and Downey and Fellows ’ Whierarchy. On a more abstract level, we consider two forms of definability, called Fagin definability and slicewise definability, that are appropriate for describing parameterized problems. We give a characterization of the class FPT of all fixedparameter tractable problems in terms of slicewise definability in finite variable least fixedpoint logic, which is reminiscent of the ImmermanVardi Theorem characterizing the class PTIME in terms of definability in least fixedpoint logic. 1
A completeness result for reasoning with incomplete firstorder knowledge bases
 In Proc. ofKR98
, 1998
"... In previous work, Levesque proposed an extension to classical databases that would allow for a certain form of incomplete firstorder knowledge. Since this extension was sufficient to make full logical deduction undecidable, he also proposed an alternative reasoning scheme with desirable logical pro ..."
Abstract

Cited by 30 (9 self)
 Add to MetaCart
In previous work, Levesque proposed an extension to classical databases that would allow for a certain form of incomplete firstorder knowledge. Since this extension was sufficient to make full logical deduction undecidable, he also proposed an alternative reasoning scheme with desirable logical properties. He also claimed (without proof) that this reasoning could be implemented efficiently using database techniques such as projections and joins. In this paper, we substantiate this claim and show how to adapt a bottomup database query evaluation algorithm for this purpose, thus obtaining a tractability result comparable to those that exist for databases. The rest of the paper is organized as follows. In the next section, we review proper KBs and V, prove a new property of V, i.e. locality, and define answers to open queries. In Section 3, we review the complexity of database query evaluation, and present a polynomial time algorithm for evaluating Kguarded formulas. In Section 4, we show how to use this algorithm to evaluate queries wrt proper KBs and hence obtain a tractability result. In Section 5, we illustrate this query evaluation method for proper KBs with some example queries. Finally in Section 6, we describe some future work. 1
Hypertree decompositions: A survey
 In: MFCS ’01: Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
, 2001
"... Abstract. This paper surveys recent results related to the concept of hypertree decomposition and the associated notion of hypertree width. A hypertree decomposition of a hypergraph (similar to a tree decomposition of a graph) is a suitable clustering of its hyperedges yielding a tree or a forest. I ..."
Abstract

Cited by 29 (4 self)
 Add to MetaCart
Abstract. This paper surveys recent results related to the concept of hypertree decomposition and the associated notion of hypertree width. A hypertree decomposition of a hypergraph (similar to a tree decomposition of a graph) is a suitable clustering of its hyperedges yielding a tree or a forest. Important NP hard problems become tractable if restricted to instances whose associated hypergraphs are of bounded hypertree width. We also review a number of complexity results on problems whose structure is described by acyclic or nearly acyclic hypergraphs. 1