Structural effects in algorithm performance: A framework and a case study on graph coloring

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, the examination of structural properties present in the instances and the effects they have on algorithm performance are proposed; the goal is to characterize complexity in terms of instance structure. A framework for identifying and characterizing hard instances based on algorithm behaviour is proposed as well as a case study applying the framework on the graph coloring problem is presented.