The Hardness and Approximation Algorithms for L-Diversity

TL;DR

This paper provides the first theoretical analysis of l-diversity, proving NP-hardness of optimal solutions and introducing an approximation algorithm with practical effectiveness validated by experiments.

Contribution

It is the first to study the theoretical complexity of l-diversity and offers a novel approximation algorithm with proven bounds.

Findings

Optimal l-diverse generalization is NP-hard.

An (l*d)-approximation algorithm is proposed.

Experimental results validate the algorithm's effectiveness.

Abstract

The existing solutions to privacy preserving publication can be classified into the theoretical and heuristic categories. The former guarantees provably low information loss, whereas the latter incurs gigantic loss in the worst case, but is shown empirically to perform well on many real inputs. While numerous heuristic algorithms have been developed to satisfy advanced privacy principles such as l-diversity, t-closeness, etc., the theoretical category is currently limited to k-anonymity which is the earliest principle known to have severe vulnerability to privacy attacks. Motivated by this, we present the first theoretical study on l-diversity, a popular principle that is widely adopted in the literature. First, we show that optimal l-diverse generalization is NP-hard even when there are only 3 distinct sensitive values in the microdata. Then, an (l*d)-approximation algorithm is developed, where d is the dimensionality of the underlying dataset. This is the first known algorithm with a non-trivial bound on information loss. Extensive experiments with real datasets validate the effectiveness and efficiency of proposed solution.