In search of the best constraint satisfaction search
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
The hardest constraint problems: a double phase transition
Artificial Intelligence
Exploiting the deep structure of constraint problems
Artificial Intelligence
Sudden emergence of a giant k-core in a random graph
Journal of Combinatorial Theory Series B
A Sufficient Condition for Backtrack-Free Search
Journal of the ACM (JACM)
Results related to threshold phenomena research in satisfiability: lower bounds
Theoretical Computer Science - Phase transitions in combinatorial problems
Lower bounds for random 3-SAT via differential equations
Theoretical Computer Science - Phase transitions in combinatorial problems
Exact phase transitions in random constraint satisfaction problems
Journal of Artificial Intelligence Research
A probabilistic analysis of randomly generated binary constraint satisfaction problems
Theoretical Computer Science
The satisfiability threshold for randomly generated binary constraint satisfaction problems
Random Structures & Algorithms
Many hard examples in exact phase transitions
Theoretical Computer Science
Random constraint satisfaction: Easy generation of hard (satisfiable) instances
Artificial Intelligence
A Model to Study Phase Transition and Plateaus in Relational Learning
ILP '08 Proceedings of the 18th international conference on Inductive Logic Programming
Empirical Study of Relational Learning Algorithms in the Phase Transition Framework
ECML PKDD '09 Proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases: Part I
Consistency and random constraint satisfaction models
Journal of Artificial Intelligence Research
A simple model to generate hard satisfiable instances
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Phase Transition in the Bandwidth Minimization Problem
MICAI '09 Proceedings of the 8th Mexican International Conference on Artificial Intelligence
On the phase transitions of random k-constraint satisfaction problems
Artificial Intelligence
Exact thresholds for DPLL on random XOR-SAT and NP-complete extensions of XOR-SAT
Theoretical Computer Science
Challenging heuristics: evolving binary constraint satisfaction problems
Proceedings of the 14th annual conference on Genetic and evolutionary computation
A general model and thresholds for random constraint satisfaction problems
Artificial Intelligence
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The standard models used to generate random binary constraint satisfaction problems are described. At the problem sizes studied experimentally, a phase transition is seen as the constraint tightness is varied. However, Achlioptas et al. showed that if the problem size (number of variables) increases while the remaining parameters are kept constant, asymptotically almost all instances are unsatisfiable. In this paper, an alternative scheme for one of the standard models is proposed in which both the number of values in each variable's domain and the average degree of the constraint graph are increased with problem size. It is shown that with this scheme there is asymptotically a range of values of the constraint tightness in which instances are trivially satis-able with probability at least 0.5 and a range in which instances are almost all unsatisfiable; hence there is a crossover point at some value of the constraint tightness between these two ranges. This scheme is compared to a similar scheme due to Xu and Li.