Studying the Effects of Instance Structure in Algorithm Performance

of Paper to be published in the Proceedings of Complexity, Cybernetics, and Informing Science and Engineering PORTUGALan IIIS Conference collocated with InSITE After the conference is over, the International Institute of Informatics and Systemics (IIIS, www.iiis.org Studying the Effects of Instance Structure in Algorithm Performance Tania Turrubiates-Lopez Instituto Tecnologico Superior de Alamo Temapache, Alamo, Veracruz, Mexico tania251179@gmail.com Satu-Elisa Schaeffer Universidad Autonoma de Nuevo Leon, San Nicolas de los Garza, Nuevo Leon, Mexico elisa.schaeffer@gmail.com Abstract 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.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.