Predicting algorithmic complexity through structure analysis and compression

Abstract

The complexity of an algorithm is usually speci ed by the maximum number of steps made by the algorithm, as a function of the size of the input. However, as di erent inputs of equal size can yield dramatically di erent algorithm runtime, the size of the input is not always an appropriate basis for predicting algorithm runtime. In this paper, we argue that the compressed size of the input is more appropriate for this purpose. In particular, we devise a genetic algorithm for compressing a graph by nding the most compact description of its structure, and we demonstrate how the compressed size of the problem instance correlates with the runtime of an exact algorithm for two hard combinatorial problems (graph coloring and Boolean satis ability).