A Generic Scheme for the Design of Efficient On-Line Algorithms for Lattices
A major issue with large dynamic datasets is the processing of small changes in the input through correspondingly small rearrangements of the output. This was the motivation behind the design of incremental or on-line algorithms for lattice maintenance, whose work amounts to a gradual construction of the final lattice by repeatedly adding rows/columns to the data table. As an attempt to put the incremental trend on strong theoretical grounds, we present a generic algorithmic scheme that is based on a detailed analysis of the lattice transformation triggered by a row/column addition and of the underlying sub-structure. For each task from the scheme we suggest an efficient implementation strategy and put a lower bound on its worst-case complexity. Moreover, an instanciation of the incremental scheme is presented which is as complex as the best batch algorithm.
KeywordsBinary Relation Lower Cover Formal Concept Analysis Hasse Diagram Incremental Algorithm
Unable to display preview. Download preview PDF.
- 1.Barbut, M., Monjardet, B.: Ordre et Classification: Algèbre et combinatoire. Hachette (1970)Google Scholar
- 3.Carpineto, C., Romano, G.: A Lattice Conceptual Clustering System and Its Application to Browsing Retrieval. Machine Learning 24(2), 95–122 (1996)Google Scholar
- 4.Ganter, B.: Two basic algorithms in concept analysis, Technische Hochschule, Darmstadt (1984) (preprint 831)Google Scholar
- 6.Godin, R., Mili, H.: Building and maintaining analysis-level class hierarchies using Galois lattices. In: Proceedings of OOPSLA 1993, Washington (DC), Special issue of ACM SIGPLAN Notices vol. 28(10), pp. 394–410 (1993)Google Scholar
- 9.Kuznetsov, S., Ob’edkov, S.: Algorithms for the Construction of the Set of All Concept and Their Line Diagram. preprint MATH-AL-05-2000, Technische Universität, Dresden (June 2000)Google Scholar
- 12.Valtchev, P., Missaoui, R.: A Framework for Incremental Generation of Frequent Closed Itemsets. Discrete Applied Mathematics (submitted)Google Scholar