Analyzing the impact of knowledge on algorithm performance in discrete optimization

For discrete optimization, it is important to understand the relationship between knowledge about the characteristics of problems and algorithm performance. Such an understanding will provide us useful hints and better prediction of algorithm behavior when we choose or design algorithms. In this paper, we seek to formally model and analyze the impact of such knowledge on algorithm performance/behavior, We propose a model which we call the Directional Tree (DT) to explore this impact. With DTs, we provide the first steps in formally explaining knowledge and algorithm behavior through rigorous proofs and analysis.