On the average case analysis of some satisfiability model problems
Information Sciences: an International Journal
On the probabilistic performance of algorithms for the satisfiability problem
Information Processing Letters
Polynomial-average-time satisfiability problems
Information Sciences: an International Journal
A survey of average time analyses of satisfiability algorithms
Journal of Information Processing
Elimination of infrequent variables improves average case performance of satisfiability algorithms
SIAM Journal on Computing
SIAM Journal on Computing
Backtrack programming techniques
Communications of the ACM
An Average Analysis of Backtracking on Random Constraint Satisfaction Problems
Annals of Mathematics and Artificial Intelligence
Exact phase transitions in random constraint satisfaction problems
Journal of Artificial Intelligence Research
Hi-index | 0.00 |
The average running time used by backtracking on random constraint satisfaction problems is studied. This time is polynomial when the ratio of constraints to variables is large, and it is exponential when the ratio is small. When the number of variables goes to infinity, whether the average time is exponential or polynomial depends on the number of variables per constraint, the number of values per variable, and the probability that a random setting of variables satisfies a constraint. A method for computing the curve that separates polynomial from exponential time and several methods for approximating the curve are given. The version of backtracking studied finds all solutions to a problem, so the running time is exponential when the number of solutions per problem is exponential. For small values of the probability, the curve that separates exponential and polynomial average running time coincides with the curve that separates an exponential average number of solutions from a polynomial number. For larger probabilities the two curves diverge. Random problems similar to those that arise in understanding line drawings with shadows require a time that is mildly exponential when they are solved by simple backtracking. Slightly more sophisticated algorithms (such as constraint propagation combined with backtracking) should be able to solve these rapidly.