Are friends of my friends too social? Limitations of location privacy in a socially-connected world

With the ubiquitous adoption of smartphones and mobile devices, it is now common practice for one's location to be sensed, collected and likely shared through social platforms. While such data can be helpful for many applications, users start to be aware of the privacy issue in handling location and trajectory data. While some users may voluntarily share their location information (e.g., for receiving location-based services, or for crowdsourcing systems), their location information may lead to information leaks about the whereabouts of other users, through the co-location of events when two users are at the same location at the same time and other side information, such as upper bounds of movement speed. It is therefore crucial to understand how much information one can derive about other's positions through the co-location of events and occasional GPS location leaks of some of the users. In this paper we formulate the problem of inferring locations of mobile agents, present theoretically-proven bounds on the amount of information that could be leaked in this manner, study their geometric nature, and present algorithms matching these bounds. We will show that even if a very weak set of assumptions is made on trajectories' patterns, and users are not obliged to follow any 'reasonable' patterns, one could infer very accurate estimation of users' locations even if they opt not to share them. Furthermore, this information could be obtained using almost linear-time algorithms, suggesting the practicality of the method even for huge volumes of data.