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 Hypergraph Properties for Constraint Satisfaction and Conjunctive Queries
Journal of the ACM (JACM)
On the complexity of existential positive queries
ACM Transactions on Computational Logic (TOCL)
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The way the graph structure of the constraints influences the complexity of constraint satisfaction problems (CSP) is well understood for bounded-arity constraints. The situation is less clear if there is no bound on the arities. In this case the answer depends also on how the constraints are represented in the input. We study this question for the truth table representation of constraints. We introduce a new hypergraph measure adaptive width and show that CSP with truth tables is polynomial-time solvable if restricted to a class of hypergraphs with bounded adaptive width. Conversely, assuming a conjecture on the complexity of binary CSP, there is no other polynomial-time solvable case. Finally, we present a class of hypergraphs with bounded adaptive width and unbounded fractional hypertree width.