Summarizing CSP Hardness with Continuous Probability Distributions

Abstract

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. 1. Introduction Several key developments in the 1990's have contributed to the advancement of empirical research on CSP algorithms, to the extent that the field may even be called an experimental science. Striking increases in computer power and decreases in cost, coupled with the general adoption of C as the programming language of choice, have made it possible for the developer of a new algorithm or heuristic to test it on large numbers of random instances. Another important advance was the recognition of the "50% satisfi...