Ionizing radiation can damage cells by breaking both strands of DNA in multiple locations, essentially cutting chromosomes into pieces. The cell has enzymatic mechanisms to repair such breaks; however, these mechanisms are imperfect and, in an exchange process, may produce a large-scale rearrangement of the genome, called a chromosome aberration. Chromosome aberrations are important in killing cells, during carcinogenesis, in characterizing repair/misrepair pathways, in retrospective radiation biodosimetry, and in a number of other ways. DNA staining techniques such as mFISH (multicolor fluorescent in situ hybridization) provide a means for analyzing aberration spectra by examining observed final patterns. Unfortunately, an mFISH observed final pattern often does not uniquely determine the underlying exchange process. Further, resolution limitations in the painting protocol sometimes lead to apparently incomplete final patterns. We here describe an algorithm for systematically finding exchange processes consistent with any observed final pattern. This algorithm uses aberration multigraphs, a mathematical formalism that links the various aspects of aberration formation. By applying a measure to the space of consistent multigraphs, we will show how to generate model-specific distributions of aberration processes from mFISH experimental data. The approach is implemented by software freely available over the internet. As a sample application, we apply these algorithms to an aberration data set, obtaining a distribution of exchange cycle sizes, which serves to measure aberration complexity. Estimating complexity, in turn, helps indicate how damaging the aberrations are and may facilitate identification of radiation type in retrospective biodosimetry.