Decomposing constraint satisfaction problems using database techniques
Artificial Intelligence
Generating hard satisfiability problems
Artificial Intelligence - Special volume on frontiers in problem solving: phase transitions and complexity
A comparison of structural CSP decomposition methods
Artificial Intelligence
The complexity of acyclic conjunctive queries
Journal of the ACM (JACM)
Constraint Processing
Many hard examples in exact phase transitions
Theoretical Computer Science
Random constraint satisfaction: Easy generation of hard (satisfiable) instances
Artificial Intelligence
A unified theory of structural tractability for constraint satisfaction problems
Journal of Computer and System Sciences
On balanced CSPs with high treewidth
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Measuring the hardness of SAT instances
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Exact phase transitions in random constraint satisfaction problems
Journal of Artificial Intelligence Research
Consistency and random constraint satisfaction models
Journal of Artificial Intelligence Research
Where the really hard problems are
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 1
On the power of structural decompositions of graph-based representations of constraint problems
Artificial Intelligence
Constraint Networks: Techniques and Algorithms
Constraint Networks: Techniques and Algorithms
Hard and easy distributions of SAT problems
AAAI'92 Proceedings of the tenth national conference on Artificial intelligence
Phase transition of tractability in constraint satisfaction and bayesian network inference
UAI'03 Proceedings of the Nineteenth conference on Uncertainty in Artificial Intelligence
A note on treewidth in random graphs
COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
A general model and thresholds for random constraint satisfaction problems
Artificial Intelligence
Variable-Centered Consistency in Model RB
Minds and Machines
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Consider random hypergraphs on n vertices, where each k-element subset of vertices is selected with probability p independently and randomly as a hyperedge. By sparse we mean that the total number of hyperedges is O(n) or O(n ln n). When k = 2, these are exactly the classical Erdös-Rényi random graphs G(n, p). We prove that with high probability, hinge width on these sparse random hypergraphs can grow linearly with the expected number of hyperedges. Some random constraint satisfaction problems such as Model RB and Model RD have satisfiability thresholds on these sparse constraint hypergraphs, thus the large hinge width results provide some theoretical evidence for random instances around satisfiability thresholds to be hard for a standard hinge-decomposition based algorithm. We also conduct experiments on these and other kinds of random graphs with several hundreds vertices, including regular random graphs and power law random graphs. The experimental results also show that hinge width can grow linearly with the number of edges on these different random graphs. These results may be of further interests.