The organization of large-scale repositories of learning objects with directed hypergraphs

In this paper we focus on the problem of finding personalized learning paths in presence of a large number of available learning components. In particular, we model the relationships holding between learning activities and the related (needed/achieved) competence, based on directed hypergraphs. We show as the complexity of optimizing learning paths depends dramatically on the adopted metrics; in particular, we prove that finding a learning path with minimum timespan can be done in quasi-linear time, whilst finding one with minimum total effort (apparently, a very similar problem) is NP-hard. Therefore in some cases, it is possible to use simple and fast algorithms for computing personalized elearning paths, while in other cases the developers must rely on approximated heuristics, or adequate computational resources. We are implementing this modeling and the related algorithms in the framework provided by the LECOMPS system for personalized e-learning. The final aim is to apply the modeling in large repositories, or in wider web-based e-learning environments.