Some intersection theorems for ordered sets and graphs
Journal of Combinatorial Theory Series A
On the Desirability of Acyclic Database Schemes
Journal of the ACM (JACM)
Degrees of acyclicity for hypergraphs and relational database schemes
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
Which problems have strongly exponential complexity?
Journal of Computer and System Sciences
Fixed-parameter complexity in AI and nonmonotonic reasoning
Artificial Intelligence
Properties of acyclic database schemes
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
Optimal implementation of conjunctive queries in relational data bases
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
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
Partitioning multi-dimensional sets in a small number of "Uniform" parts
European Journal of Combinatorics
Algorithms for acyclic database schemes
VLDB '81 Proceedings of the seventh international conference on Very Large Data Bases - Volume 7
Hypertree width and related hypergraph invariants
European Journal of Combinatorics
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
On tree width, bramble size, and expansion
Journal of Combinatorial Theory Series B
Approximating fractional hypertree width
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
The structure of tractable constraint satisfaction problems
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Approximating rank-width and clique-width quickly
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Parameterized Complexity
Constraint satisfaction problems and global cardinality constraints
Communications of the ACM
Structural tractability of enumerating CSP solutions
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
Structural tractability of constraint optimization
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
The complexity of conservative valued CSPs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Computing hypergraph width measures exactly
Information Processing Letters
Journal of Computer and System Sciences
Worst-case optimal join algorithms: [extended abstract]
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
Constraint satisfaction problems: convexity makes all different constraints tractable
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
Constraint optimization problems and bounded tree-width revisited
CPAIOR'12 Proceedings of the 9th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Decomposing Quantified Conjunctive (or Disjunctive) Formulas
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Counting homomorphisms via hypergraph-based structural restrictions
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
Tractable triangles and cross-free convexity in discrete optimisation
Journal of Artificial Intelligence Research
Constraint satisfaction problems: Convexity makes AllDifferent constraints tractable
Theoretical Computer Science
The tractability of CSP classes defined by forbidden patterns
Journal of Artificial Intelligence Research
The complexity of conservative valued CSPs
Journal of the ACM (JACM)
The fine classification of conjunctive queries and parameterized logarithmic space complexity
Proceedings of the 32nd symposium on Principles of database systems
Tractable counting of the answers to conjunctive queries
Journal of Computer and System Sciences
The complexity of finite-valued CSPs
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Block-Sorted quantified conjunctive queries
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
The complexity of weighted counting for acyclic conjunctive queries
Journal of Computer and System Sciences
Tractable Hypergraph Properties for Constraint Satisfaction and Conjunctive Queries
Journal of the ACM (JACM)
Robust Satisfiability for CSPs: Hardness and Algorithmic Results
ACM Transactions on Computation Theory (TOCT)
On the complexity of existential positive queries
ACM Transactions on Computational Logic (TOCL)
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An important question in the study of constraint satisfaction problems (CSP) is understanding how the graph or hypergraph describing the incidence structure of the constraints influences the complexity of the problem. For binary CSP instances (i.e., where each constraint involves only two variables), the situation is well understood: the complexity of the problem essentially depends on the treewidth of the graph of the constraints. However, this is not the correct answer if constraints with unbounded number of variables are allowed, and in particular, for CSP instances arising from query evaluation problems in database theory. Formally, if H is a class of hypergraphs, then let CSP(H) be CSP restricted to instances whose hypergraph is in H. Our goal is to characterize those classes of hypergraphs for which CSP(H) is polynomial-time solvable or fixed-parameter tractable, parameterized by the number of variables. In the applications related to database query evaluation, we usually assume that the number of variables is much smaller than the size of the instance, thus parameterization by the number of variables is a meaningful question. The most general known property of H that makes CSP(H) polynomial-time solvable is bounded fractional hypertree width. Here we introduce a new hypergraph measure called submodular width, and show that bounded submodular width of H (which is a strictly more general property than bounded fractional hypertree width) implies that CSP(H) is fixed-parameter tractable. In a matching hardness result, we show that if H has unbounded submodular width, then CSP(H) is not fixed-parameter tractable (and hence not polynomial-time solvable), unless the Exponential Time Hypothesis (ETH) fails. The algorithmic result uses tree decompositions in a novel way: instead of using a single decomposition depending on the hypergraph, the instance is split into a set of instances (all on the same set of variables as the original instance), and then the new instances are solved by choosing a different tree decomposition for each of them. The reason why this strategy works is that the splitting can be done in such a way that the new instances are "uniform" with respect to the number extensions of partial solutions, and therefore the number of partial solutions can be described by a submodular function. For the hardness result, we prove via a series of combinatorial results that if a hypergraph H has large submodular width, then a 3SAT instance can be efficiently simulated by a CSP instance whose hypergraph is H. To prove these combinatorial results, we need to develop a theory of (multicommodity) flows on hypergraphs and vertex separators in the case when the function b(S) defining the cost of separator S is submodular.