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 A1Example, min(S.Price) <= v  is succinct But, sum(S.Price) >= v  is not succinctI 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 !
Why is sum a succinct constraint?
data mining
We can show that the sum above threshold is not succinct by providing a counter example.As you wrote the definition isGiven 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 A1Hence, 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) >= 3For 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.