Statistical analysis of backtracking on inconsistent CSPs
We analyze the distribution of computational effort required by backtracking algorithms on unsatisfiable CSPs, using analogies with reliability models, where lifetime of a specimen before failure corresponds to the runtime of backtracking on unsatisfiable CSPs. We extend the results of  by showing empirically that the lognormal distribution is a good approximation of the backtracking effort on unsolvable CSPs not only at the 50% satisfiable point, but in a relatively wide region. We also show how the law of proportionate effect  commonly used to derive the lognormal distribution can be applied to modeling the number of nodes expanded in a search tree. Moreover, for certain intervals of C/N, where N is the number of variables, and C is the number of constraints, the parameters of the corresponding lognormal distribution can be approximated by the linear lognormal model  where mean log(deadends) is linear in C/N, and variance of log(deadends) is close to constant. The linear lognormal model allows us to extrapolate the results from a relativelyeasy overconstrained region to the hard critically constrained region and, in particular, to use more efficient strategies for testing backtracking algorithms.
KeywordsLognormal Distribution Search Tree Constraint Satisfaction Problem Proportionate Effect Maximum Likelihood Estimator
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