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arXiv · 1110.6739

The Binary Perfect Phylogeny with Persistent characters

Paola Bonizzoni·Chiara Braghin·Riccardo Dondi·Gabriella Trucco
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Abstract

The binary perfect phylogeny model is too restrictive to model biological events such as back mutations. In this paper we consider a natural generalization of the model that allows a special type of back mutation. We investigate the problem of reconstructing a near perfect phylogeny over a binary set of characters where characters are persistent: characters can be gained and lost at most once. Based on this notion, we define the problem of the Persistent Perfect Phylogeny (referred as P-PP). We restate the P-PP problem as a special case of the Incomplete Directed Perfect Phylogeny, called Incomplete Perfect Phylogeny with Persistent Completion, (refereed as IP-PP), where the instance is an incomplete binary matrix M having some missing entries, denoted by symbol ?, that must be determined (or completed) as 0 or 1 so that M admits a binary perfect phylogeny. We show that the IP-PP problem can be reduced to a problem over an edge colored graph since the completion of each column of the input matrix can be represented by a graph operation. Based on this graph formulation, we develop an exact algorithm for solving the P-PP problem that is exponential in the number of characters and polynomial in the number of species.

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Paola Bonizzoni, Chiara Braghin, Riccardo Dondi, Gabriella Trucco. 2012-06-28. The Binary Perfect Phylogeny with Persistent characters. https://arxiv.org/abs/1110.6739

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