The advent of social networks poses severe threats on user privacy as adversaries can de-anonymize users' identities by mapping them to correlated cross-domain networks. Without ground-truth mapping, prior literature proposes various cost functions in hope of measuring the quality of mappings. However, there is generally a lacking of rationale behind the cost functions, whose minimizer also remains algorithmically unknown. We jointly tackle above concerns under a more practical social network model parameterized by overlapping communities, which, neglected by prior art, can serve as side information for de-anonymization. Regarding the unavailability of ground-truth mapping to adversaries, by virtue of the Minimum Mean Square Error (MMSE), our first contribution is a well-justified cost function minimizing the expected number of mismatched users over all possible true mappings. While proving the NP-hardness of minimizing MMSE, we validly transform it into the weighted-edge matching problem (WEMP), which, as disclosed theoretically, resolves the tension between optimality and complexity: (i) WEMP asymptotically returns a negligible mapping error in large network size under mild conditions facilitated by higher overlapping strength; (ii) WEMP can be algorithmically characterized via the convex-concave based de-anonymization algorithm (CBDA), finding the optimum of WEMP. Extensive experiments further confirm the effectiveness of CBDA under overlapping communities, in terms of averagely 90% re-identified users in the rare true cross-domain co-author networks when communities overlap densely, and roughly 70% enhanced reidentification ratio compared to non-overlapping cases.

A crucial privacy-driven issue nowadays is re- identifying ano-nymized social networks by mapping them to correlated cross-domain auxiliary networks. Prior works are typically based on modeling social networks as random graphs representing users and their relations, and subsequently quantify the quality of mappings through cost functions that are proposed without sufficient rationale. Also, it remains unknown how to algorithmically meet the demand of such quantifications, i.e., to find the minimizer of the cost functions. We address those concerns in a more realistic social network modeling parameterized by community structures that can be leveraged as side information for de- anonymization. By Maximum A Posteriori (MAP) estimation, our first contribution is new and well justified cost functions, which, when minimized, enjoy superiority to previous ones in finding the correct mapping with the highest probability. The feasibility of the cost functions is then for the first time algorithmically characterized. While proving the general multiplicative inapproximability, we are able to propose two heuristics, which, respectively, enjoy an ε-additive approximation and a conditional optimality in carrying out successful user re- identification. Our theoretical findings are empirically validated,with a notable dataset extracted from rare true cross-domain networks that reproduce genuine social network de-anonymization.