Algorithms for Comparing Pedigree Graphs

Pedigree graphs, which represent family relationships, are often constructed by collecting data from genealogical records to determine which pairs of people are parent and child. This process is expensive, and small mistakes in data collection–for example, one missing parent-child relationship–can cause large differences in the pedigree graphs created. In this paper, we introduce a simple pedigree definition based on a different type of data which is potentially easier to collect. This alternative characterization of a pedigree that describes a pedigree as a list of the descendants of each individual, rather than a list of parent-child relationships. We then introduce an algorithm that generates the pedigree graph from this list of descendants. We also consider the problem of comparing two pedigree graphs, which could be useful to evaluate the differences between pedigrees constructed via different methods. Specifically, this could be useful to evaluate pedigree reconstruction methods. We define the edit distance between two pedigrees and prove that calculating this edit distance is APX-hard. Our new characterization of a pedigree allows us to introduce a fast heuristic for the edit distance between pedigrees. In addition we introduce several exact algorithms for calculating distances in restricted and general cases.