Summarizing CSP Hardness with Continuous Probability Distributions

We present empirical evidence that the distribution of effort required to solve CSPs randomly generated at the 50% satisfiable point, when using a backtracking algorithm, can be approximated by two standard families of continuous probability distribution functions. Solvable problems can be modelled by the Weibull distribution, and unsolvable problems by the lognormal distribution. These distributions fit equally well over a variety of backtracking based algorithms.

我们提供了经验证据，即在使用回溯算法时，可以在50％令人满意点上随机生成的CSP所需的努力分布，可以由两个连续概率分布函数的标准家族近似。可解决的问题可以通过Weibull分布来建模，而无法解决的问题通过对数正态分布进行建模。这些分布在各种基于回溯的算法上同样符合。