The invention provides methods for identifying rare variants near a structural variation in a genetic sequence, for example, in a nucleic acid sample taken from a subject. The invention additionally includes methods for aligning reads (e.g., nucleic acid reads) to a reference sequence construct accounting for the structural variation, methods for building a reference sequence construct accounting for the structural variation or the structural variation and the rare variant, and systems that use the alignment methods to identify rare variants. The method is scalable, and can be used to align millions of reads to a construct thousands of bases long, or longer.