The invention provides methods for comparing one set of genetic sequences to another without discarding any information within either set. A set of genetic sequences is represented using a directed acyclic graph (DAG) avoiding any unwarranted reduction to a linear data structure. The invention provides a way to align one sequence DAG to another to produce an alignment that can itself be stored as a DAG. DAG-to-DAG alignment is a natural choice wherever a set of genomic information consisting of more than one string needs to be compared to any non-linear reference. For example, a subpopulation DAG could be compared to a population DAG in order to compare the genetic features of that subpopulation to those of the population.