Tree clustering for constraint networks (research note)
Artificial Intelligence
The monadic second-order logic of graphs VII: graphs as relational structures
Theoretical Computer Science - Special issue on logic and applications to computer science
Graph searching and a min-max theorem for tree-width
Journal of Combinatorial Theory Series B
Decomposing constraint satisfaction problems using database techniques
Artificial Intelligence
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Complexity of answering queries using materialized views
PODS '98 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Hypertree decompositions and tractable queries
PODS '99 Proceedings of the eighteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Acyclic hypergraph projections
Journal of Algorithms
Constraint satisfaction and database theory: a tutorial
PODS '00 Proceedings of the nineteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Information integration using logical views
Theoretical Computer Science - Special issue on the 6th International Conference on Database Theory—ICDT '97
Conjunctive query containment revisited
Theoretical Computer Science - Special issue on the 6th International Conference on Database Theory—ICDT '97
Conjunctive-query containment and constraint satisfaction
Journal of Computer and System Sciences - Special issue on the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on principles of database systems
A comparison of structural CSP decomposition methods
Artificial Intelligence
When is the evaluation of conjunctive queries tractable?
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
The complexity of acyclic conjunctive queries
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ACM Transactions on Computational Logic (TOCL)
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Foundations of Databases: The Logical Level
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STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
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The parameterized complexity of database queries
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Query evaluation via tree-decompositions
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Games and Model Checking for Guarded Logics
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Hypertree Decompositions: A Survey
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
Grounding for model expansion in k-guarded formulas with inductive definitions
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
A tractability result for reasoning with incomplete first-order knowledge bases
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Declarative programming of search problems with built-in arithmetic
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
A greedy algorithm for constructing a low-width generalized hypertree decomposition
Proceedings of the 13th International Conference on Database Theory
On the complexity of model expansion
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
PBINT, a logic for modelling search problems involving arithmetic
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Hypertree decompositions: structure, algorithms, and applications
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
On the complexity of entailment in existential conjunctive first-order logic with atomic negation
Information and Computation
The dag-width of directed graphs
Journal of Combinatorial Theory Series B
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In a previous paper [10], the authors introduced the notion of hypertree decomposition and the corresponding concept of hypertree width and showed that the conjunctive queries whose hypergraphs have bounded hypertree-width can be evaluated in polynomial time. Bounded hypertree-width generalizes the notions of acyclicity and bounded treewidth and corresponds to larger classes of tractable queries. In the present paper, we provide natural characterizations of hypergraphs and queries having bounded hypertree-width in terms of game-theory and logic.First we define the Robber and Marshals game, and prove that a hypergraph H has hypertree-width at most k iff k marshals have a winning strategy on H, allowing them to trap a robber who moves along the hyperedges. This game is akin the well-known Robber and Cops game (which characterizes bounded treewidth), except that marshals are more powerful than cops: They can control entire hyperedges instead of just vertices.Kolaitis and Vardi [17] recently gave an elegant characterization of the conjunctive queries having treewidth k in terms of the k-variable fragment of a certain logic L ( = existential-conjunctive fragment of positive FO). We use the Robber and Marshals game to derive a surprisingly simple and equally elegant characterization of the class HW[k] of queries of hypertree-width at most k in terms of guarded logic. In particular, we show that HW[k] = GFk (L), where GFk(L) denotes the k-guarded fragment of L. In this fragment, conjunctions of k atoms rather than just single atoms are allowed to act as guards. Note that, for the particular case k = 1, our results provide new characterizations of the class of acyclic queries.We extend the notion of bounded hypertreewidth to nonrecursive stratified datalog and show that the k-guarded fragment GFk(FO) of first order logic has the same expressive power as nonrecursive stratified datalog of hypertreewidth ⪇ k.