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Information leakageis usually defined as the logarithmic increment in the adversary’s probability of correctly guessing the legitimate user’s private data or some arbitrary function of the private data when presented with the legitimate user’s publicly disclosed information. However, this definition of information leakage implicitly assumes that both the privacy mechanism and the prior probability of the original data are entirely known to the attacker. In reality, the assumption of complete knowledge of the privacy mechanism for an attacker is often impractical. The attacker can usually have access to only an approximate version of the correct privacy mechanism, computed from a limited set of the disclosed data, for which they can access the corresponding un-distorted data. In this scenario, the conventional definition of leakage no longer has an operational meaning. To address this problem, in this article, we propose novel meaningful information-theoretic metrics for information leakage when the attacker hasincomplete informationabout the privacy mechanism—we call themaverage subjective leakage,average confidence boost, andaverage objective leakage, respectively. For the simplest, binary scenario, we demonstrate how to find an optimized privacy mechanism that minimizes the worst-case value of either of these leakages.

Recommending a Point of Interest (PoI) or a sequence of PoIs to visit based on user’s preferences and geo-locations has been one of the most popular applications of Location-Based Services (LBS). Variants have also been considered which take other factors into consideration, such as broader (implicit or explicit) semantic constraints as well as the limitations on the length of the trip. In this work, we present an efficient algorithmic solution to a novel query –PaDOC(Paths with Distance, Origin, and Category constraints) – which combines the generation of a path that (a) can be traversed within a user-specified budget (e.g., limit on distance), (b) starts at one of the user-specified origin locations (e.g., a hotel), and (c) contains PoIs from a user-specified list of PoI categories. We show that the problem of deciding whether such a path exists is an NP-hard problem. Based on a novel indexing structure, we propose two efficient algorithms for approximatePaDOCquery processing based on both conservative and progressive distance estimations. We conducted extensive experiments over real, publicly available datasets, demonstrating the benefits of the proposed methodologies over straightforward solutions.