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People increasingly share personal information, including their photos and photo collections, on social media. This information, however, can compromise individual privacy, particularly as social media platforms use it to infer detailed models of user behavior, including tracking their location. We consider the specific issue of location privacy as potentially revealed by posting photo collections, which facilitate accurate geolocation with the help of deep learning methods even in the absence of geotags. One means to limit associated inadvertent geolocation privacy disclosure is by carefully pruning select photos from photo collections before these are posted publicly. We study this problem formally as a combinatorial optimization problem in the context of geolocation prediction facilitated by deep learning. We first demonstrate the complexity both by showing that a natural greedy algorithm can be arbitrarily bad and by proving that the problem is NP-Hard. We then exhibit an important tractable special case, as well as a more general approach based on mixed-integer linear programming. Through extensive experiments on real photo collections, we demonstrate that our approaches are indeed highly effective at preserving geolocation privacy.