On generating all maximal independent sets
Information Processing Letters
Arboricity and bipartite subgraph listing algorithms
Information Processing Letters
Reengineering class hierarchies using concept analysis
SIGSOFT '98/FSE-6 Proceedings of the 6th ACM SIGSOFT international symposium on Foundations of software engineering
A fast algorithm for building lattices
Information Processing Letters
Formal Concept Analysis: Mathematical Foundations
Formal Concept Analysis: Mathematical Foundations
Fast vertical mining using diffsets
Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining
Concept Data Analysis: Theory and Applications
Concept Data Analysis: Theory and Applications
The complexity of mining maximal frequent itemsets and maximal frequent patterns
Proceedings of the tenth ACM SIGKDD international conference on Knowledge discovery and data mining
Efficient Algorithms for Mining Closed Itemsets and Their Lattice Structure
IEEE Transactions on Knowledge and Data Engineering
ACSC '06 Proceedings of the 29th Australasian Computer Science Conference - Volume 48
ISMIS '09 Proceedings of the 18th International Symposium on Foundations of Intelligent Systems
A convexity upper bound for the number of maximal bicliques of a bipartite graph
Discrete Applied Mathematics
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Concept lattices (also called Galois lattices) have been applied in numerous areas, and several algorithms have been proposed to construct them. Generally, the input for lattice construction algorithms is a binary matrix with size |G||M| representing binary relation I茂戮驴 G×M. In this paper, we consider polynomial delay algorithms for building concept lattices. Although the concept lattice may be of exponential size, there exist polynomial delay algorithms for building them. The current best delay-time complexity is O(|G||M|2). In this paper, we introduce the notion of irregular concepts, the combinatorial structure of which allows us to develop a linear delay lattice construction algorithm, that is, we give an algorithm with delay time of O(|G||M|). Our algorithm avoids the union operation for the attribute set and does not require checking if new concepts are already generated. In addition, we propose a compact representation for concept lattices and a corresponding construction algorithm. Although we are not guaranteed to achieve optimal compression, the compact representation can save significant storage space compared to the full representation normally used for concept lattices.