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I'm new to data mining and have been going through constraint-based query mining lately. I came across the concept of succinctness which basically details a constraint as succinct, if we can generate all the candidate item-sets precisely, based on an itemset satisfying the constraint.

A more formal definition is :

Given A1, the set of items satisfying a succinctness constraint C, then any set S satisfying C is based on A1 , i.e., S contains a subset belonging to A1

Example, min(S.Price) <= v is succinct
But, sum(S.Price) >= v is not succinct

I understand why the former is a succinct constraint => as all the candidates can be generated by ensuring that one of the subsets satisfies that constraint. But I fail to understand why the latter is not a succinct constraint. Any pointers on this would be helpful !

abora
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Shubham Mittal
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1 Answers1

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We can show that the "sum above threshold" is not succinct by providing a counter example.

As you wrote the definition is

Given A1, the set of items satisfying a succinctness constraint C, then any set S satisfying C is based on A1 , i.e., S contains a subset belonging to A1

Hence, we can provide a counter example by providing a set A1 satisfying the constraint while none of its subsets satisfying it.

Consider three items, a,b and c such that each one on them costs 1. Let the constraint C be sum(S.Price) >= 3

For the set {a, b, c} the sum of prices is 3 and therefore the constraint C is satisfied. For each of the subsets of {a, b, c} the sum of prices is lower than 3 and therefore C is not satisfied. We found a counter example in which a set satisfies a "sum above threshold" while none of its subsets satisfies it. Hence, "sum above threshold" is not succinct.

DaL
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