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

On analyzing and evaluating privacy measures for social networks under active attack

“…This paper does not introduce any new privacy model or measure, but simply investigates, both theoretically and empirically, computational problems for a model that is published in "Information Sciences, 328, 403-417, 2016" (reference [43]). There have been several other subsequent papers investigating this privacy measure, e.g., see [9,44,49,34]. Thus, researchers in network privacy are certainly interested in this model or related computational complexity questions.…”

“…The authors in [9] formalized and analyzed the computational complexities of several optimization problems motivated by the (k, )-anonymity of a network as described in [43]. The notations and terminologies from [9] 3 The notations and the theoretical frameworks are actually not that complicated once one goes over them carefully.…”

“…Chatterjee et al in [9] (see also [49]) formalized and analyzed the computational complexities of several optimization problems motivated by the (k, )anonymity of a network as described in [43]. In this article, we consider three of these optimization problems from [9], namely Problems 1-3 as defined in Section 2.…”

“…Chatterjee et al in [9] (see also [49]) formalized and analyzed the computational complexities of several optimization problems motivated by the (k, )anonymity of a network as described in [43]. In this article, we consider three of these optimization problems from [9], namely Problems 1-3 as defined in Section 2. A high-level itemized overview of the contribution of this article is as follows (see Section 3 for precise technical statements and details of all contributions): Our theoretical result concerning the anonymity issues for networks without cycles is provided in Theorem 1 in Section 3.1.…”

“…In Section 3.2, we first describe briefly efficient implementations of the high-level algorithms of Chatterjee et al [9] for Problems 1-3 (namely Algorithms I and II in Section 3.2.1). We then tabulate and discuss the results of applying these implemented algorithms for the following type of network data: eight real social networks listed in Table 3 in Section 3.4.2, the classical undirected Erdös-Rényi random networks G(n, p) for four suitable combinations of n and p, and the scale-free random networks G(n, q) generated by the Barábasi-Albert preferential-attachment model for four suitable combinations of n and q.…”