Measures on Sat Landscapes by Statistical Exploration of Search Trees

Stochastic local search methods are widely used for solving positive instances of NP-hard problems. They are based on a partial exploration of a local search landscape characterized by a nite set, a tness function and a neighborhood relation. We think that theoretical or experimental study of these landscapes, independently of search algorithms , could provide a better understanding of local search systems behaviour. In this paper, we propose a statistical method for measuring some parameters of landscapes. 1 For a given tness value, our algorithm gives the number of points with this tness, and produces a simple random sample of these points. As an example, we give estimates of local extrema proportion according to the tness for some SAT landscapes.