A Parallel Algorithm for Lattice Construction
The construction of the concept lattice of a context is a time consuming process. However, in many practical cases where FCA has proven to provide theoretical strength, e.g., in data mining, the volume of data to analyze is huge. This fact emphasizes the need for efficient lattice manipulations. The processing of large datasets has often been approached with parallel algorithms and some preliminary studies on parallel lattice construction exist in the literature. We propose here a novel divide-and-conquer (D&C) approach that operates by data slicing. In this paper, we present a new parallel algorithm, called DAC-ParaLaX, which borrows its main operating primitives from an existing sequential procedure and integrates them into a multi-process architecture. The algorithm has been implemented using a parallel dialect of the C ++ language and its practical performances have been compared to those of a homologue sequential algorithm.
Unable to display preview. Download preview PDF.
- 2.Foster, I.: Designing and Building Parallel Program. Addison-Wesley, Reading (1995)Google Scholar
- 4.Ganter, B.: Two basic algorithms in concept analysis. Preprint 831, Technische Hochschule, Darmstadt (1984)Google Scholar
- 6.Gropp, W., Lusk, E., Skjellum, A.: Using MPI: Portable parallel programming with the Message Passing Interface. MIT Press, Cambridge (1994)Google Scholar
- 8.LAM/MPI Team: LAM/MPI User Guide, version 7.0.4. Pervasive Technology labs, Indiana University (2004)Google Scholar
- 9.MPICH home page: (2004), http://www.mpich.org
- 10.Ndoundam, R., Njiwoua, P., Mephu Nguifo, E.: Une étude comparative de la parallélisation d’algorithmes de construction de treillis de Galois. Atelier francophone de la plate forme de l’AFIA: Usage des treillis de Galois pour l’intelligence artificielle, ESIEA Recherche (2003)Google Scholar
- 11.Njiwoua, P., Mephu Nguifo, E.: A Parallel Algorithm to build Concept Lattice. In: Proc. of the 4th Groningen Int. Information Tech. Conf. for students (1997)Google Scholar
- 13.Robson, R.: Using the STL: The C++ Standard Template Library, 2nd edn. Springer, New York (2000)Google Scholar
- 16.Tchuenté, M.: Parallel computation on rectangular arrays. Manchester University Press, Willey (1992)Google Scholar
- 18.Valtchev, P., Duquenne, V.: Towards scalable divide-and-conquer methods for computing concepts and implications. Preprint submitted to Discrete Applied Mathematics (2004)Google Scholar
- 19.Wille, R.: Restructuring lattice theory: An approach based on hierarchies of concepts. In: Rival, I. (ed.) Ordered sets, pp. 445–470. Dordrecht, Boston (1982)Google Scholar