The Organization of Large-Scale Repositories of Learning Objects with Directed Hypergraphs

  • Luigi LauraEmail author
  • Umberto Nanni
  • Marco Temperini
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8699)


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, by adopting directed hypergraph. 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 e-learning 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.


  1. 1.
    Alimonti, P., Feuerstein, E., Laura, L., Nanni, U.: Linear time analysis of properties of conflict-free and general petri nets. Theor. Comput. Sci. 412(4–5), 320–338 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Ausiello, G.: Directed hypergraphs: data structures and applications. In: Dauchet, M., Nivat, M. (eds.) CAAP 1988. LNCS, vol. 299, pp. 295–303. Springer, Heidelberg (1988)CrossRefGoogle Scholar
  3. 3.
    Ausiello, G., Italiano, G.F., Laura, L., Nanni, U., Sarracco, F.: Structure theorems for optimum hyperpaths in directed hypergraphs. In: Mahjoub, A.R., Markakis, V., Milis, I., Paschos, V.T. (eds.) ISCO 2012. LNCS, vol. 7422, pp. 1–14. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  4. 4.
    Ausiello, G., Italiano, G.F., Nanni, U.: Dynamic maintenance of directed hypergraphs. Theor. Comput. Sci. 72(2–3), 97–117 (1990)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Ausiello, G., Italiano, G.F., Nanni, U.: Hypergraph traversal revisited: cost measures and dynamic algorithms. In: Brim, L., Gruska, J., Zlatuška, J. (eds.) MFCS 1998. LNCS, vol. 1450, pp. 1–16. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  6. 6.
    Berge, C.: Graphs and Hypergraphs. Elsevier, Amsterdam (1973)zbMATHGoogle Scholar
  7. 7.
    Bergenthum, R., Desel, J., Harrer, A., Mauser, S.: Modeling and mining of learnflows. In: Jensen, K., Donatelli, S., Kleijn, J. (eds.) ToPNoC V. LNCS, vol. 6900, pp. 22–50. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  8. 8.
    Bloom, B.E.: Taxonomy of Educational Objectives. D.McKay Company Inc., New York (1964)Google Scholar
  9. 9.
    De Marsico, M., Sterbini, A., Temperini, M.: A framework to support social-collaborative personalized e-learning. In: Kurosu, M. (ed.) HCII/HCI 2013, Part II. LNCS, vol. 8005, pp. 351–360. Springer, Heidelberg (2013)Google Scholar
  10. 10.
    Gallo, G., Longo, G., Nguyen, S., Pallottino, S.: Directed hypergraphs and applications. Discrete Appl. Math. 42, 177–201 (1993)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Gallo, G., Pallottino, S.: Hypergraph models and algorithms for the assembly problem. Technical report 06/92, Dip. di Informatica, University of Pisa, Italy, Corso Italia 40, I-56125 Pisa, Italy (1992)Google Scholar
  12. 12.
    Li, H., Hasegawa, S., Kashihara, A.: A resource organization system for self-directed & community-based learning with a case study. In: Wong, L.-H. et al. (eds.) I. A.-P. S. for Computers in Education, Proceedings of the 21st International Conference on Computers in Education - ICCE 2013, pp. 329–338 (2013)Google Scholar
  13. 13.
    Limongelli, C., Sciarrone, F., Temperini, M., Vaste, G.: The lecomps5 framework for personalized web-based learning: a teacher’s satisfaction perspective. Comput. Human Behav. 27(4), 1285–1466 (2011)CrossRefGoogle Scholar
  14. 14.
    Liu, X.-Q., Wu, M., Chen, J.-X.: Knowledge aggregation and navigation high-level petri nets-based in e-learning. In: International Conference on Machine Learning and Cybernetics, vol. 1, pp. 420–425 (2002)Google Scholar
  15. 15.
    Sun, X., Lu, Y.: Directed-hypergraph based personalized e-learning process and resource optimization. In: 2012 Fourth International Conference on Digital Home (ICDH), pp. 171–178, (Nov 2012)Google Scholar
  16. 16.
    Xuedong, S., Feng, Z.: Unified and integrated e-learning modeling supporting dynamic learning process optimization. In: Eighth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD), vol. 4, pp. 2137–2141 (July 2011)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of Computer, Control, and Management Engineering Antonio RubertiSapienza UniversityRomaItaly
  2. 2.Research Centre for Transport and Logistics (CTL)Sapienza UniversityRomaItaly

Personalised recommendations