On the fine structure of large search spaces

Abstract

Recently, there has been significant progress in our understanding of the computational nature of combinatorial problems. Randomized search methods, both complete and incomplete, often outperform deterministic strategies. In this paper, we relate the performance of randomized methods to the geometric properties of the underlying search space. In particular, our study reveals the inherent fractal nature of the search space at different-length scales, for a range of combinatorial problems. We also discuss the impact of these results on the design of better search methods.