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Metric Differential Privacy (mDP) extends the local differential privacy (LDP) framework to metric spaces, enabling more nuanced privacy protection for data such as geo-locations. However, existing mDP optimization methods, particularly those based on linear programming (LP), face scalability challenges due to the quadratic growth in decision variables. In this paper, we propose Perturbation via Anchor-based Distributed Approximation (PAnDA), a scalable two-phase framework for optimizing metric differential privacy (mDP). To reduce computational overhead, PAnDA allows each user to select a small set of anchor records, enabling the server to solve a compact linear program over a reduced domain. We introduce three anchor selection strategies, exponential decay (PAnDA-e), power-law decay (PAnDA-p), and logistic decay (PAnDA-l), and establish theoretical guarantees under a relaxed privacy notion called probabilistic mDP (PmDP). Experiments on real-world geo-location datasets demonstrate that PAnDA scales to secret domains with up to 5,000 records, two times larger than prior LP-based methods, while providing theoretical guarantees for both privacy and utility. 

Geo-obfuscation serves as a location privacy protection mechanism (LPPM), enabling mobile users to share obfuscated locations with servers, rather than their exact locations. This method can protect users’ location privacy when data breaches occur on the server side since the obfuscation process is irreversible. To reduce the utility loss caused by data obfuscation, linear programming (LP) is widely employed, which, however, might suffer from a polynomial explosion of decision variables, rendering it impractical in largescale geo-obfuscation applications. In this paper, we propose a new LPPM, called Locally Relevant Geo-obfuscation (LR-Geo), to optimize geo-obfuscation using LP in a time-efficient manner. This is achieved by confining the geoobfuscation calculation for each user exclusively to the locally relevant (LR) locations to the user’s actual location. Given the potential risk of LR locations disclosing a user’s actual whereabouts, we enable users to compute the LP coefficients locally and upload them only to the server, rather than the LR locations. The server then solves the LP problem based on the received coefficients. Furthermore, we refine the LP framework by incorporating an exponential obfuscation mechanism to guarantee the indistinguishability of obfuscation distribution across multiple users. Based on the constraint structure of the LP formulation, we apply Benders’ decomposition to further enhance computational efficiency. Our theoretical analysis confirms that, despite the geo-obfuscation being calculated independently for each user, it still meets geo-indistinguishability constraints across multiple users with high probability. Finally, the experimental results based on a real-world dataset demonstrate that LR-Geo outperforms existing geo-obfuscation methods in computational time, data utility, and privacy preservation. 

We present a nanofluidic device enabling single-molecule confinement through free-energy landscapes created by dynamic electrical gating of embedded nanoelectrodes. Unlike static geometric confinement, this system uses a parallel electrode configuration with nanoelectrodes placed in a dielectric layer. Localized electrokinetic fields at electrode wells form tunable attractive potential wells for bimolecular capture. By modulating the voltage bias waveform, the device allows precise control over confinement dynamics, enabling molecular capture, release, and exposure to periodic or stochastic confinement regimes. This flexibility facilitates the study of biomolecular behavior under dynamically adjustable conditions, including controlled confinement fluctuations. The device can manipulate diverse analytes such as double-stranded DNA, liposomes, and DNA nanotubes and facilitates introducing molecules into confined environments intact from bulk while providing enhanced tunability. With the ability to implement tailored confinement profiles, this platform represents a versatile tool for probing molecular confinement and behavior in complex, dynamically varying environments.