High-throughput “next generation” genome sequencing technologies are producing a flood of inexpensive genetic information that is invaluable to genomics research. Sequences of millions of genetic markers are being produced, providing genomics researchers with the opportunity to construct highresolution genetic maps for many complicated genomes. However, the current generation of genetic mapping tools were designed for the small data setting, and are now limited by the prohibitively slow clustering algorithms they employ in the genetic markerclustering stage. In this work, we present a new approach to genetic mapping based on a fast clustering algorithm that exploits the geometry of the data. Our theoretical and empirical analysis shows that the algorithm can correctly recover linkage groups. Using synthetic and real-world data, including the grandchallenge wheat genome, we demonstrate that our approach can quickly process orders of magnitude more genetic markers than existing tools while retaining — and in some cases even improving — the quality of genetic marker clusters.