The use of next-generation sequencing technology has enabled phylogenetic studies with hun- dreds of thousands of taxa. Such large-scale phylogenies have become a critical component in genomic epidemiology in pathogens such as SARS-CoV-2 and influenza A virus. However, de- tailed phenotypic characterization of pathogens or generating a computationally tractable dataset for detailed phylogenetic analyses requires bias free subsampling of taxa. To address this need, we propose parnas, an objective and flexible algorithm to sample and select taxa that best repre- sent observed diversity by solving a generalized k-medoids problem on a phylogenetic tree. parnas solves this problem efficiently and exactly by novel optimizations and adapting algorithms from operations research. For more nuanced selections, taxa can be weighted with metadata or genetic sequence parameters, and the pool of potential representatives can be user-constrained. Motivated by influenza A virus genomic surveillance and vaccine design, parnas can be applied to identify representative taxa that optimally cover the diversity in a phylogeny within a specified distance radius. We demonstrated that parnas is more efficient and flexible than current approaches, and applied it to select representative influenza A virus in swine genes derived from over 5 years of genomic surveillance data. Our objective selection of 4 to 6 strains selected every two years from the 16 distinct genetic clades were sufficient to cover 80% of diversity circulating in US swine. We suggest that this method, through the objective selection of representatives in a phylogeny, provides criteria for rational multivalent vaccine design and for quantifying diversity. PARNAS is available at https://github.com/flu-crew/parnas.