Conditions that impact the complexity of QoS routing
IEEE/ACM Transactions on Networking (TON)
On the typical case complexity of graph optimization
Discrete Applied Mathematics - Special issue: Typical case complexity and phase transitions
Threshold properties of random boolean constraint satisfaction problems
Discrete Applied Mathematics - Special issue: Typical case complexity and phase transitions
Threshold properties of random boolean constraint satisfaction problems
Discrete Applied Mathematics
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Phase transitions in combinatorial problems have recently been shown [2] to be useful in locating 驴hard驴 instances of combinatorial problems. The connection between computational complexity and the existence of phase transitions has been addressed in Statistical Mechanics [2] and Artificial Intelligence [3], but not studied rigorously.We take a first step in this direction by investigating the existence of sharp thresholds for the class of generalized satisfiability problems, defined by Schaefer [4 ]. In the case when all constraints have a special clausal form we completely characterize the generalized satisfiability problems that have a sharp threshold. While NP-completeness does not imply the sharpness of the threshold, our result suggests that the class of counterexamples is rather limited, as all such counterexamples can be predicted, with constant success probability by a single procedure.