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103
HYPERTREE DECOMPOSITIONS AND TRACTABLE QUERIES
, 1998
"... Several important decision problems on conjunctive queries (CQs) are NPcomplete in general but become tractable, and actually highly parallelizable, if restricted to acyclic or nearly acyclic queries. Examples are the evaluation of Boolean CQs and query containment. These problems were shown tracta ..."
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Cited by 165 (42 self)
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Several important decision problems on conjunctive queries (CQs) are NPcomplete in general but become tractable, and actually highly parallelizable, if restricted to acyclic or nearly acyclic queries. Examples are the evaluation of Boolean CQs and query containment. These problems were shown tractable for conjunctive queries of bounded treewidth [7], and of bounded degree of cyclicity [18, 17]. The so far most general concept of nearly acyclic queries was the notion of queries of bounded querywidth introduced by Chekuri and Rajaraman [7]. While CQs of bounded query width are tractable, it remained unclear whether such queries are efficiently recognizable. Chekuri and Rajaraman [7] stated as an open problem whether for each constant k it can be determined in polynomial time if a query has query width ≤ k. We give a negative answer by proving this problem NPcomplete (specifically, for k = 4). In order to circumvent this difficulty, we introduce the new concept of hypertree decomposition of a query and the corresponding notion of hypertree width. We prove: (a) for each k, the class of queries with query width bounded by k is properly contained in the class of queries whose hypertree width is bounded by k; (b) unlike query width, constant hypertreewidth is efficiently recognizable; (c) Boolean queries of constant hypertree width can be efficiently evaluated.
Identifying the minimal transversals of a hypergraph and related problems
 SIAM Journal on Computing
, 1995
"... The paper considers two decision problems on hypergraphs, hypergraph saturation and recognition of the transversal hypergraph, and discusses their significance for several search problems in applied computer science. Hypergraph saturation, i.e., given a hypergraph H, decide if every subset of vertic ..."
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Cited by 155 (8 self)
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The paper considers two decision problems on hypergraphs, hypergraph saturation and recognition of the transversal hypergraph, and discusses their significance for several search problems in applied computer science. Hypergraph saturation, i.e., given a hypergraph H, decide if every subset of vertices is contained in or contains some edge of H, is shown to be coNPcomplete. A certain subproblem of hypergraph saturation, the saturation of simple hypergraphs, is shown to be computationally equivalent to transversal hypergraph recognition, i.e., given two hypergraphs H 1; H 2, decide if the sets in H 2 are all the minimal transversals of H 1. The complexity of the search problem related to the recognition of the transversal hypergraph, the computation of the transversal hypergraph, is an open problem. This task needs time exponential in the input size, but it is unknown whether an outputpolynomial algorithm exists for this problem. For several important subcases, for instance if an upper or lower bound is imposed on the edge size or for acyclic hypergraphs, we present outputpolynomial algorithms. Computing or recognizing the minimal transversals of a hypergraph is a frequent problem in practice, which is pointed out by identifying important applications in database theory, Boolean switching theory, logic, and AI, particularly in modelbased diagnosis.
An algebra for probabilistic databases
"... An algebra is presented for a simple probabilistic data model that may be regarded as an extension of the standard relational model. The probabilistic algebra is developed in such a way that (restricted to αacyclic database schemes) the relational algebra is a homomorphic image of it. Strictly prob ..."
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Cited by 149 (1 self)
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An algebra is presented for a simple probabilistic data model that may be regarded as an extension of the standard relational model. The probabilistic algebra is developed in such a way that (restricted to αacyclic database schemes) the relational algebra is a homomorphic image of it. Strictly probabilistic results are emphasized. Variations on the basic probabilistic data model are discussed. The algebra is used to explicate a commonly used statistical smoothing procedure and is shown to be potentially very useful for decision support with uncertain information.
The complexity of acyclic conjunctive queries
 Journal of the ACM
, 1998
"... This paper deals with the evaluation of acyclic Boolean conjunctive queries in relational databases. By wellknown results of Yannakakis [1981], this problem is solvable in polynomial time; its precise complexity, however, has not been pinpointed so far. We show that the problem of evaluating acyc ..."
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Cited by 96 (21 self)
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This paper deals with the evaluation of acyclic Boolean conjunctive queries in relational databases. By wellknown results of Yannakakis [1981], this problem is solvable in polynomial time; its precise complexity, however, has not been pinpointed so far. We show that the problem of evaluating acyclic Boolean conjunctive queries is complete for LOGCFL, the class of decision problems that are logspacereducible to a contextfree language. Since LOGCFL is contained in AC 1 and NC 2, the evaluation problem of acyclic Boolean conjunctive queries is highly parallelizable. We present a parallel database algorithm solving this problem with a logarithmic number of parallel join operations. The algorithm is generalized to computing the output of relevant classes of nonBoolean queries. We also show that the acyclic versions of the following wellknown database and AI problems are all LOGCFLcomplete: The Query Output Tuple problem for conjunctive queries, Conjunctive Query Containment, Clause Subsumption, and Constraint Satisfaction. The LOGCFLcompleteness result is extended to the class of queries of bounded treewidth and to other relevant query classes which are more general than the acyclic queries.
Decomposing Constraint Satisfaction Problems Using Database Techniques
, 1994
"... There is a very close relationship between constraint satisfaction problems and the satisfaction of joindependencies in a relational database which is due to a common underlying structure, namely a hypergraph. By making that relationship explicit we are able to adapt techniques previously developed ..."
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Cited by 95 (25 self)
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There is a very close relationship between constraint satisfaction problems and the satisfaction of joindependencies in a relational database which is due to a common underlying structure, namely a hypergraph. By making that relationship explicit we are able to adapt techniques previously developed for the study of relational databases to obtain new results for constraint satisfaction problems. In particular, we prove that a constraint satisfaction problem may be decomposed into a number of subproblems precisely when the corresponding hypergraph satisfies a simple condition. We show that combining this decomposition approach with existing algorithms can lead to a significant improvement in efficiency.
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 ..."
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Cited by 81 (4 self)
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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 &quot; 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
A Survey of Tractable Constraint Satisfaction Problems
, 1997
"... In this report we discuss constraint satisfaction problems. These are problems in which values must be assigned to a collection of variables, subject to specified constraints. We focus specifically on problems in which the domain of possible values for each variable is finite. The report surveys the ..."
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Cited by 52 (5 self)
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In this report we discuss constraint satisfaction problems. These are problems in which values must be assigned to a collection of variables, subject to specified constraints. We focus specifically on problems in which the domain of possible values for each variable is finite. The report surveys the various conditions that have been shown to be sufficient to ensure tractability in these problems. These are broken down into three categories: ffl Conditions on the overall structure; ffl Conditions on the nature of the constraints; ffl Conditions on bounded pieces of the problem. 1 Introduction A constraint satisfaction problem is a way of expressing simultaneous requirements for values of variables. The study of constraint satisfaction problems was initiated by Montanari in 1974 [34], when he used them as a way of describing certain combinatorial problems arising in imageprocessing. It was quickly realised that the same general framework was applicable to a much wider class of probl...
Flexible Queries over Semistructured Data
 IN PODS
, 2001
"... Flexible queries facilitate, in a novel way, easy and concise querying of databases that have varying structures. Two dierent semantics, exible and semiexible, are introduced and investigated. The complexity of evaluating queries under the two semantics is analyzed. Query evaluation is polynomial in ..."
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Cited by 51 (4 self)
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Flexible queries facilitate, in a novel way, easy and concise querying of databases that have varying structures. Two dierent semantics, exible and semiexible, are introduced and investigated. The complexity of evaluating queries under the two semantics is analyzed. Query evaluation is polynomial in the size of the query, the database and the result in the following two cases. First, a semiexible DAG query and a tree database. Second, a exible tree query and a database that is any graph. Query containment and equivalence are also investigated. For the exible semantics, query equivalence is always polynomial. For the semiexible semantics, query equivalence is polynomial for DAG queries and exponential when the queries have cycles. Under the semiexible and exible semantics, two databases could be equivalent even when they are not isomorphic. Database equivalence is formally de ned and characterized. The complexity of deciding equivalences among databases is analyzed. The implications of database equivalence on query evaluation are explained.
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 ..."
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Cited by 51 (12 self)
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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.