The hardest constraint problems: a double phase transition
Artificial Intelligence
Easy problems are sometimes hard
Artificial Intelligence
On the conversion between non-binary constraint satisfaction problems
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
Boosting combinatorial search through randomization
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
Beyond NP: the QSAT phase transition
AAAI '99/IAAI '99 Proceedings of the sixteenth national conference on Artificial intelligence and the eleventh Innovative applications of artificial intelligence conference innovative applications of artificial intelligence
Heavy-Tailed Phenomena in Satisfiability and Constraint Satisfaction Problems
Journal of Automated Reasoning
Problem difficulty for tabu search in job-shop scheduling
Artificial Intelligence
Constructive generation of very hard 3-colorability instances
Discrete Applied Mathematics
A generative power-law search tree model
Computers and Operations Research
Backdoors to Combinatorial Optimization: Feasibility and Optimality
CPAIOR '09 Proceedings of the 6th International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
On balanced CSPs with high treewidth
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Depth-bounded discrepancy search
IJCAI'97 Proceedings of the Fifteenth international joint conference on Artifical intelligence - Volume 2
Conflict-directed backjumping revisited
Journal of Artificial Intelligence Research
A simple way to improve path consistency processing in interval algebra networks
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
Generating highly balanced sudoku problems as hard problems
Journal of Heuristics
Learning vector quantization for variable ordering in constraint satisfaction problems
Pattern Recognition Letters
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Many types of problem exhibit a phase transition as a problem parameter is varied, from a region where most problems are easy and soluble to a region where most problems are easy but insoluble. In the intervening phase transition region, the median problem difficulty is greatest. However, occasional exceptionally hard problems (ehps) can be found in the easy and soluble region; these problems can be much harder than any problem occurring in the phase transition. We show that, in binary constraint satisfaction problems, ehps are much more likely to occur when the constraints are sparse than when they are dense. Ehps occur when the search algorithm encounters a large insoluble subproblem at an early stage; the exceptional difficulty is due to the cost of searching the subproblem to prove insolubility. This cost can be dramatically reduced by using conflict-directed backjumping (CBJ) rather than a chronological backtracker. However, when used with forward checking and the fail-first heuristic, it is only on ehps that CBJ gives great savings over backtracking chronologically.