| Summary: | Optimal selection of samples in populations should provide the best coverage of sample variations for the available sampling resources. In populations with known genealogical connections, or pedigrees, this amounts to finding the set of samples with the largest sum of mutual distances in a genealogical tree. We present an optimal, and a faster sub-optimal, method for the selection of <i>K</i> samples from a population of <i>N</i> individuals. The optimal method works in time proportional to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><msup><mi>K</mi><mn>2</mn></msup></mrow></semantics></math></inline-formula>, and the sub-optimal in time proportional to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mi>K</mi></mrow></semantics></math></inline-formula>, which is more practical for large populations. The sub-optimal algorithm can process pedigrees of millions of individuals in a matter of minutes. With the real-life pedigrees, the difference in the quality of the output of the two algorithms is negligible. We provide the Python3 source codes for the two methods.
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