Studying the Effects of Instance Structure in Algorithm Performance

摘要

Classical computational complexity studies the asymptotic relationship between instance size and the amount of resources consumed in the worst case. However, it has become evident that the instance size by itself is an insufficient measure and that the worst-case scenario is often uninformative in practice. As a complementary analysis, we propose the examination of structural properties present in the instances and the effects they have on algorithm performance; our goal is to characterize complexity in terms of instance structure. We propose a framework for identifying and characterizing hard instances based on algorithm behaviour as well as a case study applying the framework on the graph coloring problem.