Succinct Constraints

Definition

Let Item be the set of domain items. Then, an itemset SS _j  ⊆ Item is a succinct set if SS _j can be expressed as a result of selection operation σ _p (Item), where σ is the usual selection operator and p is a selection predicate. A powerset of items SP  ⊆  2^Item is a succinct powerset if there is a fixed number of succinct sets SS ₁,...,SS _k  ⊆ Item such that SP can be expressed in terms of the powersets of SS ₁,...,SS _k 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...