  Geo-obfuscation functions as a location privacy protection mechanism (LPPM),
enabling mobile users to share obfuscated locations with servers instead of
their exact locations. This technique protects users' location privacy during
server-side data breaches since the obfuscation process is irreversible. To
minimize the utility loss caused by data obfuscation, linear programming (LP)
is widely used. However, LP can face a polynomial explosion in decision
variables, making it impractical for large-scale geo-obfuscation applications.
In this paper, we propose a new LPPM called Locally Relevant Geo-obfuscation
(LR-Geo) to optimize geo-obfuscation using LP more efficiently. This is
accomplished by restricting the geo-obfuscation calculations for each user to
locally relevant (LR) locations near the user's actual location. To prevent LR
locations from inadvertently revealing a user's true whereabouts, users compute
the LP coefficients locally and upload only these coefficients to the server,
rather than the LR locations themselves. The server then solves the LP problem
using the provided coefficients. Additionally, we enhance the LP framework with
an exponential obfuscation mechanism to ensure that the obfuscation
distribution is indistinguishable across multiple users. By leveraging the
constraint structure of the LP formulation, we apply Benders' decomposition to
further boost computational efficiency. Our theoretical analysis confirms that,
even though geo-obfuscation is calculated independently for each user, it still
adheres to geo-indistinguishability constraints across multiple users with high
probability. Finally, experimental results using a real-world dataset
demonstrate that LR-Geo outperforms existing geo-obfuscation methods in terms
of computational time, data utility, and privacy protection.
