Graphical evolution: an introduction to the theory of random graphs
Graphical evolution: an introduction to the theory of random graphs
An algorithm for finding Hamilton paths and cycles in random graphs
Combinatorica - Theory of Computing
Finding Hamilton cycles in sparse random graphs
Journal of Combinatorial Theory Series A
Welsh-Powell opposition graphs
Information Processing Letters
An extension of the multi-path algorithm for finding Hamilton cycles
Discrete Mathematics - Special volume (part two) to mark the centennial of Julius Petersen's “Die theorie der regula¨ren graphs” (“The theory of regular graphs”)
Systematic and nonsystematic search strategies
Proceedings of the first international conference on Artificial intelligence planning systems
The hardest constraint problems: a double phase transition
Artificial Intelligence
Generating Hamiltonian circuits without backtracking from errors
Theoretical Computer Science
Randomized algorithms
Intelligent backtracking on constraint satisfaction problems: experimental and theoretical results
Intelligent backtracking on constraint satisfaction problems: experimental and theoretical results
Asymptotic and finite size parameters for phase transitions: Hamiltonian circuit as a case study
Information Processing Letters
Boosting combinatorial search through randomization
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
Which search problems are random?
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
Algorithm 595: An Enumerative Algorithm for Finding Hamiltonian Circuits in a Directed Graph
ACM Transactions on Mathematical Software (TOMS)
Graph Theory With Applications
Graph Theory With Applications
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
Heavy-Tailed Phenomena in Satisfiability and Constraint Satisfaction Problems
Journal of Automated Reasoning
On the Fine Structure of Large Search Spaces
ICTAI '99 Proceedings of the 11th IEEE International Conference on Tools with Artificial Intelligence
SAT problems with chains of dependent variables
Discrete Applied Mathematics - The renesse issue on satisfiability
On the complexity of unfrozen problems
Discrete Applied Mathematics - Special issue: Typical case complexity and phase transitions
Many hard examples in exact phase transitions
Theoretical Computer Science
Exact phase transitions in random constraint satisfaction problems
Journal of Artificial Intelligence Research
Phase transitions and backbones of the asymmetric traveling salesman problem
Journal of Artificial Intelligence Research
An analysis of phase transition in NK landscapes
Journal of Artificial Intelligence Research
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Where are the really hard manipulation problems? the phase transition in manipulating the veto rule
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Efficient SAT Techniques for Relative Encoding of Permutations with Constraints
AI '09 Proceedings of the 22nd Australasian Joint Conference on Advances in Artificial Intelligence
On the complexity of unfrozen problems
Discrete Applied Mathematics
SAT-based analysis of feature models is easy
Proceedings of the 13th International Software Product Line Conference
Is computational complexity a barrier to manipulation?
CLIMA'10 Proceedings of the 11th international conference on Computational logic in multi-agent systems
An effective algorithm for and phase transitions of the directed hamiltonian cycle problem
Journal of Artificial Intelligence Research
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Using an improved backtrack algorithm with sophisticated pruning techniques, we revise previous observations correlating a high frequency of hard to solve Hamiltonian cycle instances with the Gn,m phase transition between Hamiltonicity and non-Hamiltonicity. Instead all tested graphs of 100 to 1500 vertices are easily solved. When we artificially restrict the degree sequence with a bounded maximum degree, although there is some increase in difficulty, the frequency of hard graphs is still low. When we consider more regular graphs based on a generalization of knight's tours, we observe frequent instances of really hard graphs, but on these the average degree is bounded by a constant. We design a set of graphs with a feature our algorithm is unable to detect and so are very hard for our algorithm, but in these we can vary the average degree from O(1) to O(n). We have so far found no class of graphs correlated with the Gn,m phase transition which asymptotically produces a high frequency of hard instances.