The k-anonymity Problem is Hard

Paola Bonizzoni, Gianluca Della Vedova and Riccardo Dondi

Abstract

The problem of publishing personal data without giving up privacy is 
becoming increasingly important. An interesting formalization recently 
proposed is the k-anonymity. This approach requires that the rows in a 
table are clustered in sets of size at least k and that all the rows in 
a cluster are related to the same tuple, after the suppression of some 
records. The problem has been shown to be NP-hard when the  values are 
over a ternary alphabet, k=3 and the rows length is unbounded. In this 
paper we give a lower bound on the approximation of two restrictions of 
the problem, when the records values are over a binary alphabet and k=3, 
and when the records have length at most 8 and k=4, showing that these 
restrictions of the problem are APX-hard.