Resolving the Complexity of Some Data Privacy Problems

We formally study two methods for data sanitation that have been used extensively in the database community: k-anonymity and l-diversity. We settle several open problems concerning the difficulty of applying these methods optimally, proving both positive and negative results: – 2-anonymity is in P. – The problem of partitioning the edges of a triangle-free graph into 4-stars (degree-three vertices) is NP-hard. This yields an alternative proof that 3-anonymity is NP-hard even when the database attributes are all binary. – 3-anonymity with only 27 attributes per record is MAX SNP-hard. – For databases with n rows, k-anonymity is in O(4 · poly(n))) time for all k > 1. – For databases with l attributes, alphabet size c, and n rows, k-Anonymity can be solved in 2 (2c)) +O(nl) time. – 3-diversity with binary attributes is NP-hard, with one sensitive attribute. – 2-diversity with binary attributes is NP-hard, with three sensitive attributes.