On the Computational Complexities of Three Privacy Measures for Large Networks Under Active Attack

TL;DR

This paper formalizes three privacy measures for large networks, analyzes their computational complexity, and finds that two are efficiently computable while the third is computationally hard to approximate.

Contribution

It introduces three formal privacy measures for large networks and provides the first theoretical complexity results, including efficient algorithms and hardness proofs.

Findings

Two privacy measures can be computed efficiently.

The third privacy measure is hard to approximate within a logarithmic factor.

Efficient algorithms exist for restricted privacy requirements.

Abstract

With the arrival of modern internet era, large public networks of various types have come to existence to benefit the society as a whole and several research areas such as sociology, economics and geography in particular. However, the societal and research benefits of these networks have also given rise to potentially significant privacy issues in the sense that malicious entities may violate the privacy of the users of such a network by analyzing the network and deliberately using such privacy violations for deleterious purposes. Such considerations have given rise to a new active research area that deals with the quantification of privacy of users in large networks and the corresponding investigation of computational complexity issues of computing such quantified privacy measures. In this paper, we formalize three such privacy measures for large networks and provide non-trivial theoretical computational complexity results for computing these measures. Our results show the first two measures can be computed efficiently, whereas the third measure is provably hard to compute within a logarithmic approximation factor. Furthermore, we also provide computational complexity results for the case when the privacy requirement of the network is severely restricted, including an efficient logarithmic approximation.