Data-Driven Discrete Geofence Design Using Binary Quadratic Programming

2025-09-29

AI Summary

Traditional geofencing methods rely on manually defined or idealized circular boundaries, which poorly conform to complex urban road networks and administrative boundaries, leading to overlaps and misalignment. This paper proposes a data-driven approach for automatically extracting arbitrary-shaped geofences. We formulate fence partitioning as a 0–1 integer programming problem and equivalently transform it into a Quadratic Unconstrained Binary Optimization (QUBO) formulation, enabling efficient solving via quantum annealing and other advanced optimizers. Leveraging high-resolution mobile trajectory data, our method jointly optimizes spatial connectivity, boundary fidelity, and semantic consistency within a discrete grid space. Experiments demonstrate that the generated non-circular geofences significantly improve geometric and semantic alignment with urban infrastructure—such as one-way streets and physical barriers—as well as administrative boundaries. The proposed framework provides a more flexible and robust geocoding foundation for managing high-dynamic urban spatial events.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Distributed Search
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Federated Web and WoT systems, including distributed, federated and edge-based data processing
• Security and Privacy: Data transparency and provenance

Abstract

Geofences have attracted significant attention in the design of spatial and virtual regions for managing and engaging spatiotemporal events. By using geofences to monitor human activity across their boundaries, content providers can create spatially triggered events that include notifications about points of interest within a geofence by pushing spatial information to the devices of users. Traditionally, geofences were hand-crafted by providers. In addition to the hand-crafted approach, recent advances in collecting human mobility data through mobile devices can accelerate the automatic and data-driven design of geofences, also known as the geofence design problem. Previous approaches assume circular shapes; thus, their flexibility is insufficient, and they can only handle geofence-based applications for large areas with coarse resolutions. A challenge with using circular geofences in urban and high-resolution areas is that they often overlap and fail to align with political district boundaries and road segments, such as one-way streets and median barriers. In this study, we address the problem of extracting arbitrary shapes as geofences from human mobility data to mitigate this problem. In our formulation, we cast the existing optimization problems for circular geofences to 0-1 integer programming problems to represent arbitrary shapes. Although 0-1 integer programming problems are computationally hard, formulating them as quadratic (unconstrained) binary optimization problems enables efficient approximation of optimal solutions, because this allows the use of specialized quadratic solvers, such as the quantum annealing, and other state-of-the-art algorithms. We then develop and compare different formulation methods to extract discrete geofences. We confirmed that our new modeling approach enables flexible geofence design.

Problem

• Extracting arbitrary shapes as geofences from human mobility data
• Overcoming limitations of circular geofences in urban high-resolution areas
• Formulating geofence design as quadratic binary optimization problems

Innovation

• Using binary quadratic programming for geofence design
• Formulating geofences as quadratic unconstrained binary optimization
• Extracting arbitrary shapes from human mobility data