Optical mapping (OM) is a rapidly maturing strategy for detecting large-scale rearrangements in genomes, leveraging ultra-long fragments of DNA imaged at very high depth of coverage (>100×). OM data reflect an orthogonal strategy to DNA sequencing, instead utilizing image-based detection of fluorescent tags associated with specific DNA motifs. The resulting data can be aligned back to the reference genome for discovery of genomic rearrangements and karyotypic abnormalities. Existing methods, however, are computationally demanding, making discovery harder. We present a novel method, FaNDOM, for alignment of OM data to the reference genome, and the additional discovery of structural variants. FaNDOM utilizes fast filtering algorithms based on constructing graph-based chains of seed matches, achieving orders of magnitude speedup, while maintaining high sensitivity, enabling a more comprehensive search of complex structural variations involving hundreds of kbp.