2+p-SAT: relation of typical-case complexity to the nature of the phase transition
Random Structures & Algorithms - Special issue on statistical physics methods in discrete probability, combinatorics, and theoretical computer science
New methods to color the vertices of a graph
Communications of the ACM
The phase transition in 1-in-k SAT and NAE 3-SAT
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Rigorous results for random (2 + p)-SAT
Theoretical Computer Science - Phase transitions in combinatorial problems
A Treshold for Unsatisfiability
MFCS '92 Proceedings of the 17th International Symposium on Mathematical Foundations of Computer Science
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Threshold phenomena in random graph colouring and satisfiability
Threshold phenomena in random graph colouring and satisfiability
Problem structure in the presence of perturbations
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
Communication and Computation in Distributed CSP Algorithms
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Sensor networks and distributed CSP: communication, computation and complexity
Artificial Intelligence - Special issue: Distributed constraint satisfaction
Sensor networks and distributed CSP: communication, computation and complexity
Artificial Intelligence - Special issue: Distributed constraint satisfaction
Is computational complexity a barrier to manipulation?
Annals of Mathematics and Artificial Intelligence
Where are the hard manipulation problems?
Journal of Artificial Intelligence Research
A smooth transition from powerlessness to absolute power
Journal of Artificial Intelligence Research
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We study in detail the interface between P and NP by means of five new problem classes. Like the well known 2+p-SAT problem, these new problems smoothly interpolate between P and NP by mixing together a polynomial and a NP-complete problem. In many cases, the polynomial subproblem can dominate the problem's satisfiability and the search complexity. However, this is not always the case, and understanding why remains a very interesting open question. We identify phase transition behavior in each of these problem classes. Surprisingly we observe transitions with both smooth and sharp regions. Finally we show how these problem classes can help to understand algorithm behavior by considering search trajectories through the phase space.