Improving repair-based constraint satisfaction methods by value propagation
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
Easy problems are sometimes hard
Artificial Intelligence
Scaling Effects in the CSP Phase Transition
CP '95 Proceedings of the First International Conference on Principles and Practice of Constraint Programming
Performance test of local search algorithms using new types of random CNF formulas
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Frozen development in graph coloring
Theoretical Computer Science - Phase transitions in combinatorial problems
Nonsystematic Search and No-Good Learning
Journal of Automated Reasoning
Non-systematic Search and Learning: An Empirical Study
CP '98 Proceedings of the 4th International Conference on Principles and Practice of Constraint Programming
Evolving combinatorial problem instances that are difficult to solve
Evolutionary Computation
Constructive generation of very hard 3-colorability instances
Discrete Applied Mathematics
The backdoor key: a path to understanding problem hardness
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
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
How the landscape of random job shop scheduling instances depends on the ratio of jobs to machines
Journal of Artificial Intelligence Research
Analysis of phase transitions in graph-coloring problems based on constraint structures
PRICAI'00 Proceedings of the 6th Pacific Rim international conference on Artificial intelligence
Computing infeasibility certificates for combinatorial problems through Hilbert's Nullstellensatz
Journal of Symbolic Computation
Using hajós' construction to generate hard graph 3-colorability instances
AISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Symbolic Computation
Hi-index | 0.00 |
The easy-hard-easy pattern in the difficulty of combinatorial search problems as constraints are added has been explained as due to a competition between the decrease in number of solutions and increased pruning. We test the generality of this explanation by examining one of its predictions: if the number of solutions is held fixed by the choice of problems, then increased pruning should lead to a monotonic decrease in search cost. Instead, we find the easy-hard-easy pattern in median search cost even when the number of solutions is held constant, for some search methods. This generalizes previous observations of this pattern and shows that the existing theory does not explain the full range of the peak in search cost. In these cases the pattern appears to be due to changes in the size of the minimal unsolvable subproblems, rather than changing numbers of solutions.