Phase transitions in artificial intelligence systems
Artificial Intelligence
Partial constraint satisfaction
Artificial Intelligence - Special volume on constraint-based reasoning
Performance of linear-space search algorithms
Artificial Intelligence
Phase transitions and the search problem
Artificial Intelligence - Special volume on frontiers in problem solving: phase transitions and complexity
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A machine program for theorem-proving
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Frozen development in graph coloring
Theoretical Computer Science - Phase transitions in combinatorial problems
Computers and Intractability: A Guide to the Theory of NP-Completeness
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Generating Satisfiable Problem Instances
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Backbone fragility and the local search cost peak
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Where the really hard problems are
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 1
Backbones in optimization and approximation
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Searching for an optimal path in a tree with random costs
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Clustering at the phase transition
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
Effort profiles in multi-agent resource allocation
Proceedings of the first international joint conference on Autonomous agents and multiagent systems: part 1
Comparing phase transitions and peak cost in PP-complete satisfiability problems
Eighteenth national conference on Artificial intelligence
Searching for backbones and fat: a limit-crossing approach with applications
Eighteenth national conference on Artificial intelligence
MaxSolver: an efficient exact algorithm for (weighted) maximum satisfiability
Artificial Intelligence
Discrete Applied Mathematics - Special issue: Typical case complexity and phase transitions
Complexity of Max-SAT using stochastic algorithms
Proceedings of the 10th annual conference on Genetic and evolutionary computation
Probabilistic logic with independence
International Journal of Approximate Reasoning
Improving Performance in Combinatorial Optimisation Using Averaging and Clustering
EvoCOP '09 Proceedings of the 9th European Conference on Evolutionary Computation in Combinatorial Optimization
Empirical hardness models: Methodology and a case study on combinatorial auctions
Journal of the ACM (JACM)
Backbones and backdoors in satisfiability
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 3
Relaxed survey propagation: a sum-product algorithm for Max-SAT
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Phase transitions and backbones of the asymmetric traveling salesman problem
Journal of Artificial Intelligence Research
Backbone guided local search for maximum satisfiability
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Phase transitions of bounded satisfiability problems
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Phase transitions of the asymmetric traveling salesman
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
The backbone of the travelling salesperson
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
MaxSolver: An efficient exact algorithm for (weighted) maximum satisfiability
Artificial Intelligence
Discrete Applied Mathematics
Relaxed survey propagation for the weighted maximum satisfiability problem
Journal of Artificial Intelligence Research
Learning the large-scale structure of the MAX-SAT landscape using populations
IEEE Transactions on Evolutionary Computation
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Many real-world problems involve constraints that cannot be all satisfied. Solving an overconstrained problem then means to find solutions minimizing the number of constraints violated, which is an optimization problem. In this research, we study the behavior of the phase transitions and backbones of constraint optimization problems. We first investigate the relationship between the phase transitions of Boolean satisfiability, or precisely 3-SAT (a well-studied NP-complete decision problem), and the phase transitions of MAX 3-SAT (an NP-hard optimization problem). To bridge the gap between the easy-hard-easy phase transitions of 3-SAT and the easy-hard transitions of MAX 3-SAT, we analyze bounded 3-SAT, in which solutions of bounded quality, e.g., solutions with at most a constant number of constraints violated, are sufficient. We show that phase transitions are persistent in bounded 3-SAT and are similar to that of 3-SAT. We then study backbones of MAX 3-SAT, which are critically constrained variables that have fixed values in all optimal solutions. Our experimental results show that backbones of MAX 3-SAT emerge abruptly and experience sharp transitions from nonexistence when underconstrained to almost complete when overconstrained. More interestingly, the phase transitions of MAX 3-SAT backbones seem to concur with the phase transitions of satisfiability of 3-SAT. The backbone of MAX 3-SAT with size 0.5 approximately collocates with the 0.5 satisfiability of 3-SAT, and the backbone and satisfiability seems to follow a linear correlation near this 0.5-0.5 collocation.