Definition
Let Item be the set of domain items. Then, an itemset SSj ⊆ Item is a succinct set if SSj can be expressed as a result of selection operation σp(Item), where σ is the usual selection operator and p is a selection predicate. A powerset of items SP ⊆ 2Item is a succinct powerset if there is a fixed number of succinct sets SS1, …, SSk ⊆ Item such that SP can be expressed in terms of the powersets of SS1, …, SSk using set union and/or set difference operators. A constraint C is succinct provided that the set of itemsets satisfying C is a succinct powerset.
Key Points
Succinct constraints [1, 2] possess the following nice properties. For any succinct constraint C, there exists a precise “formula” – called a member generating function (MGF) – to enumerate all and only those itemsets that are guaranteed to satisfy C. Hence, if C is succinct, then C is pre-counting prunable. This means that one can directly generate precisely the itemsets that satisfy C– without looking at the...
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Recommended Reading
Lakshmanan LVS, Leung CK-S, Ng RT. Efficient dynamic mining of constrained frequent sets. ACM Trans Database Syst. 2003;28(4):337–89. https://doi.org/10.1145/958942.958944.
Ng RT, Lakshmanan LVS, Han J, Pang A. Exploratory mining and pruning optimizations of constrained associations rules. In: Proceedings of the ACM SIGMOD International Conference on Management of Data; 1998. p. 13–24.
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Leung, C.KS. (2018). Succinct Constraints. In: Liu, L., Özsu, M.T. (eds) Encyclopedia of Database Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8265-9_5049
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