Resolving the complexity of some data privacy problems

Abstract

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 n •poly(n))) time for all k>1. For databases with l attributes, alphabet size c, and n rows, k-Anonymity can be solved in 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. © 2010 Springer-Verlag Berlin Heidelberg.