Statistical Analysis of Backtracking on Inconsistent CSPs

Abstract

Abs t r ac t . 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 [7] 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 o] proportionate effect [9] 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 [11] 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 relatively easy overconstrained region to the hard critically constrained region and, in particular, to use more efficient strategies for testing backtracking algorithms.

DOI: 10.1007/BFb0017436

Cite this paper

@inproceedings{Rish1997StatisticalAO, title={Statistical Analysis of Backtracking on Inconsistent CSPs}, author={Irina Rish and Daniel Frost}, booktitle={CP}, year={1997} }