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In contrast to other mutations, duplication leaves an easily detectable trace: a repetition. Therefore it is a convenient starting point for computing a phylogenetic network. Basically, all squares must be detected to compute all possible direct predecessors. To find all the possible, not necessarily direct predecessors, this process must be iterated for all the resulting strings. We show how to reuse the work for one string in this process for the detection of squares in all the strings that are derived from it. For the detection of squares we propose suffix arrays as data structure and show how they can be updated after the reduction of a square.
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