Let A be an m × n binary matrix, t ∈ {1,…,m} be a threshold, and ε > 0 be a positive parameter. We show that given a family of O(nε) maximal t-frequent column sets for A, it is NP-complete to decide whether A has any further maximal t-frequent sets, or not, even when the number of such additional maximal t-frequent column sets may be exponentially large. In contrast, all minimal t-infrequent sets of columns of A can be enumerated in incremental quasi-polynomial time. The proof of the latter result follows from the inequality α ≤ (m-t +1)β, where α and β are respectively the numbers of all maximal t-frequent and all minimal t-infrequent sets of columns of the matrix A. We also discuss the complexity of generating all closed t-frequent column sets for a given binary matrix.
CITATION STYLE
Boros, E., Gurvich, V., Khachiyan, L., & Makino, K. (2002). On the complexity of generating maximal frequent and minimal infrequent sets. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2285, pp. 133–141). Springer Verlag. https://doi.org/10.1007/3-540-45841-7_10
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