Some intersection theorems for ordered sets and graphs
Journal of Combinatorial Theory Series A
Approximating treewidth, pathwidth, frontsize, and shortest elimination tree
Journal of Algorithms
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
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
When is the evaluation of conjunctive queries tractable?
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Approximation algorithms
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
A Combinatorial Proof of Kneser’s Conjecture
Combinatorica
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)
Approximating clique-width and branch-width
Journal of Combinatorial Theory Series B
The complexity of homomorphism and constraint satisfaction problems seen from the other side
Journal of the ACM (JACM)
Journal of Combinatorial Theory Series B
Generalized hypertree decompositions: np-hardness and tractable variants
Proceedings of the twenty-sixth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Hypertree width and related hypergraph invariants
European Journal of Combinatorics
The structure of tractable constraint satisfaction problems
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Hypertree decompositions: structure, algorithms, and applications
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Approximating rank-width and clique-width quickly
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Generalized hypertree decompositions: NP-hardness and tractable variants
Journal of the ACM (JACM)
On the power of structural decompositions of graph-based representations of constraint problems
Artificial Intelligence
Tractable hypergraph properties for constraint satisfaction and conjunctive queries
Proceedings of the forty-second ACM symposium on Theory of computing
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
Factorised representations of query results: size bounds and readability
Proceedings of the 15th International Conference on Database Theory
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Fractional hypertree width is a hypergraph measure similar to tree width and hypertree width. Its algorithmic importance comes from the fact that, as shown in previous work [14], constraint satisfaction problems (CSP) and various problems in database theory are polynomial-time solvable if the input contains a bounded-width fractional hypertree decomposition of the hypergraph of the constraints. In this paper, we show that for every w ≥ 1, there is a polynomial-time algorithm that, given a hypergraph H with fractional hypertree width at most w, computes a fractional hypertree decomposition of width O(w3) for H. This means that polynomial-time algorithms relying on bounded-width fractional hypertree decompositions no longer need to be given a decomposition explicitly in the input, since an appropriate decomposition can be computed in polynomial time. Therefore, if H is a class of hypergraphs with bounded fractional hypertree width, then CSP restricted to instances whose structure is in H is polynomial-time solvable. This makes bounded fractional hypertree width the most general known hypergraph property that makes CSP, Boolean Conjuctive Queries, and Conjunctive Query Containment polynomial-time solvable.