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Prior research developed Reassortment Networks to reconstruct the evolution of segmented viruses under both reassortment and mutation. We report their application to the swine-origin pandemic H1N1 virus (S-OIV). A database of all influenza A viruses, for which complete genome sequences were available in Genbank by October 2009, was created and dynamic programming was used to compute distances between all corresponding segments. A reassortment network was created to obtain the minimum cost evolutionary paths from all viruses to the exemplar S-OIV A/California/04/2009. This analysis took 35 hours on the Cray Extreme Multithreading (XMT) supercomputer, which has special hardware to permit efficient parallelization. Six specific H1N1/H1N2 bottleneck viruses were identified that almost always lie on minimum cost paths to S-OIV. We conjecture that these viruses are crucial to S-OIV evolution and worthy of careful study from a molecular biology viewpoint. In phylogenetics, ancestors are typically medians that have no functional constraints. In our method, ancestors are not inferred, but rather chosen from previously observed viruses along a path of mutation and reassortment leading to the target virus. This specificity and functional constraint render our results actionable for further experiments in vitro and in vivo.