A Large Version of the Small Parsimony Problem

Given a multiple alignment over k sequences, an evolutionary tree relating the sequences, and a subadditive gap penalty function (e.g. an affine function), we reconstruct the internal nodes of the tree optimally: we find the optimal explanation in terms of indels of the observed gaps and find the most parsimonious assignment of nucleotides. The gaps of the alignment are represented in a so-called gap graph, and through theoretically sound preprocessing the graph is reduced to pave the way for a running time which in all but the most pathological examples is far better than the exponential worst case time. E.g. for a tree with nine leaves and a random alignment of length 10.000 with 60% gaps, the running time is on average around 45 seconds. For a real alignment of length 9868 of nine HIV-1 sequences, the running time is less than one second.

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