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A constraint C is monotone if and only if for all itemsets S and S′:
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Monotone constraints [1–3] possess the following property. If an itemset S violates a monotone constraint C, then any of its subsets also violates C. Equivalently, all supersets of an itemset satisfying a monotone constraint C also satisfy C (i.e., C is upward closed). By exploiting this property, monotone constraints can be used for reducing computation in frequent itemset mining with constraints. As frequent itemset mining with constraints aims to find frequent itemsets that satisfy the constraints, if an itemset S satisfies a monotone constraint C, no further constraint checking needs to be applied to any superset of S because all supersets of S are guaranteed to satisfy C. Examples of monotone constraints include min(S. Price) ≤ $30, which expresses that the...
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Brin S., Motwani R., and Silverstein C. Beyond market baskets: generalizing association rules to correlations. In Proc. ACM SIGMOD Int. Conf. on Management of Data, 1997, pp. 265–276.
Grahne G., Lakshmanan L.V.S., and Wang X. Efficient mining of constrained correlated sets. In Proc. 16th Int. Conf. on Data Engineering, 2000, pp. 512–521.
Pei J. and Han J. Can we push more constraints into frequent pattern mining? In Proc. 6th ACM SIGKDD Int. Conf. on Knowledge Discovery and Data Mining, 2000, pp. 350–354.
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Leung, CS. (2009). Monotone Constraints. In: LIU, L., ÖZSU, M.T. (eds) Encyclopedia of Database Systems. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-39940-9_5048
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DOI: https://doi.org/10.1007/978-0-387-39940-9_5048
Publisher Name: Springer, Boston, MA
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