Efficient algorithms for combinatorial problems on graphs with bounded, decomposability—a survey
BIT - Ellis Horwood series in artificial intelligence
Closures of database hypergraphs
Journal of the ACM (JACM)
Easy problems for tree-decomposable graphs
Journal of Algorithms
Graph rewriting: an algebraic and logic approach
Handbook of theoretical computer science (vol. B)
Solving queries by tree projections
ACM Transactions on Database Systems (TODS)
Journal of Algorithms
Acyclic hypergraph projections
Journal of Algorithms
On the Desirability of Acyclic Database Schemes
Journal of the ACM (JACM)
Syntactic Characterization of Tree Database Schemas
Journal of the ACM (JACM)
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
The complexity of acyclic conjunctive queries
Journal of the ACM (JACM)
Symbolic Logic and Mechanical Theorem Proving
Symbolic Logic and Mechanical Theorem Proving
Foundations of Databases: The Logical Level
Foundations of Databases: The Logical Level
Query evaluation via tree-decompositions
Journal of the ACM (JACM)
Optimal implementation of conjunctive queries in relational data bases
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
Robbers, marshals, and guards: game theoretic and logical characterizations of hypertree width
Journal of Computer and System Sciences - Special issu on PODS 2001
Weighted hypertree decompositions and optimal query plans
PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Constraint solving via fractional edge covers
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
On the complexity of combinatorial auctions: structured item graphs and hypertree decomposition
Proceedings of the 8th ACM conference on Electronic commerce
Algorithms for acyclic database schemes
VLDB '81 Proceedings of the seventh international conference on Very Large Data Bases - Volume 7
A unified theory of structural tractability for constraint satisfaction problems
Journal of Computer and System Sciences
Marshals, monotone marshals, and hypertree-width
Journal of Graph Theory
Tree Projections: Hypergraph Games and Minimality
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Approximating fractional hypertree width
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Bounded treewidth as a key to tractability of knowledge representation and reasoning
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
A unified theory of structural tractability for constraint satisfaction and spread cut decomposition
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
A greedy algorithm for constructing a low-width generalized hypertree decomposition
Proceedings of the 13th International Conference on Database Theory
Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Structural tractability of enumerating CSP solutions
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
Approximation algorithms for domination search
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
Structural tractability of constraint optimization
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
H-DB: a hybrid quantitative-structural sql optimizer
Proceedings of the 20th ACM international conference on Information and knowledge management
Efficient approximations of conjunctive queries
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
Counting homomorphisms via hypergraph-based structural restrictions
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
Information and Computation
Structural tractability of counting of solutions to conjunctive queries
Proceedings of the 16th International Conference on Database Theory
Theoretical Computer Science
Skew strikes back: new developments in the theory of join algorithms
ACM SIGMOD Record
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The generalized hypertree width GHW(H) of a hypergraph H is a measure of its cyclicity. Classes of conjunctive queries or constraint satisfaction problems whose associated hypergraphs have bounded GHW are known to be solvable in polynomial time. However, it has been an open problem for several years if for a fixed constant k and input hypergraph H it can be determined in polynomial time whether GHW(H) ≤ k. Here, this problem is settled by proving that even for k = 3 the problem is already NP-hard. On the way to this result, another long standing open problem, originally raised by Goodman and Shmueli [1984] in the context of join optimization is solved. It is proven that determining whether a hypergraph H admits a tree projection with respect to a hypergraph G is NP-complete. Our intractability results on generalized hypertree width motivate further research on more restrictive tractable hypergraph decomposition methods that approximate generalized hypertree decomposition (GHD). We show that each such method is dominated by a tractable decomposition method definable through a function that associates a set of partial edges to a hypergraph. By using one particular such function, we define the new Component Hypertree Decomposition method, which is tractable and strictly more general than other approximations to GHD published so far.