Objectives: Crime prevention strategies often rely on the small set of micro-places where crime is most concentrated, the so-called hotspots, yet it has remained unclear how close existing hotspot detection methods come to the maximum coverage theoretically possible. This study introduces GraphVenn, the first algorithm that identifies the globally optimal placement of N fixed-radius hotspots directly from the empirical crime distribution, without relying on heuristic or approximate approaches.

Methods: GraphVenn was evaluated on three years of crime data from Malm & ouml;, Boston, and New York City (in total 1.75 million crimes) and compared against kernel density estimation (KDE), greedy PAI maximization (PAI-Max), and GraphTrace. Both the globally optimal and the greedy (fast approximation) modes of GraphVenn were evaluated across different spatial resolutions, demonstrating scalability to large urban datasets.

Results: In optimal mode, GraphVenn identified the absolute maximum coverage of incidents achievable under fixed-radius constraints. The greedy variant reached within 0.1-1.9% of this optimum while reducing runtimes by up to two orders of magnitude. By contrast, existing methods consistently fell short, e.g., in New York City the optimal GraphVenn captured 51,522 crimes within its top-100 hotspots compared to 35,098 with KDE and 28,241 with GraphTrace, while PAI-Max was excluded due to its runtimes. In practical terms, the baselines therefore missed between 16,000 and 23,000 crime incidents that could have been covered.

Conclusions: Globally optimal detection of fixed-radius hotspots that maximize the distinct crime count is now computationally feasible at city scale. GraphVenn offers (i) a practical tool for researchers, law enforcement, and crime analysts to identify the most effective fixed-radius hotspot locations with confidence that no better configuration exists, and (ii) a benchmark for evaluating approximate methods against the true maximum crime count. Open-source code is provided to support replication and further research.