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Identifying recombinant sequences in an era of large genomic databases is challenging as it requires an efficient algorithm to identify candidate recombinants and parents, as well as appropriate statistical methods to correct for the large number of comparisons performed. In 2007, a computation was introduced for an exact nonparametric mosaicism statistic that gave high-precision P values for putative recombinants. This exact computation meant that multiple-comparisons corrected P values also had high precision, which is crucial when performing millions or billions of tests in large databases. Here, we introduce an improvement to the algorithmic complexity of this computation from O(mn³) to O(mn²), where m and n are the numbers of recombination-informative sites in the candidate recombinant. This new computation allows for recombination analysis to be performed in alignments with thousands of …