Entry uniqueness in margined tables

Abstract

We consider a problem in secure disclosure of multiway table margins. If the value of an entry in all tables having the same margins as those released from a source table in a data base is unique, then the value of that entry can be exposed and disclosure is insecure. We settle the computational complexity of detecting whether this situation occurs. In particular, for multiway tables where one category is significantly richer than the others, that is, when each sample point can take many values in one category and only few values in the other categories, we provide, for the first time, a polynomial time algorithm for checking uniqueness, allowing disclosing agencies to check entry uniqueness and make learned decisions on secure disclosure. Our proofs use our recent results on universality of 3-way tables and on n-fold integer programming, which we survey on the way.