Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polynomial-Time Algorithms for Phylogenetic Inference Problems involving
  duplication and reticulation   A common problem in phylogenetics is to try to infer a species phylogeny from
gene trees. We consider different variants of this problem. The first variant,
called Unrestricted Minimal Episodes Inference, aims at inferring a species
tree based on a model with speciation and duplication where duplications are
clustered in duplication episodes. The goal is to minimize the number of such
episodes. The second variant, Parental Hybridization, aims at inferring a
species \emph{network} based on a model with speciation and reticulation. The
goal is to minimize the number of reticulation events. It is a variant of the
well-studied Hybridization Number problem with a more generous view on which
gene trees are consistent with a given species network. We show that these
seemingly different problems are in fact closely related and can, surprisingly,
both be solved in polynomial time, using a structure we call "beaded trees".
However, we also show that methods based on these problems have to be used with
care because the optimal species phylogenies always have a restricted form. To
mitigate this problem, we introduce a new variant of Unrestricted Minimal
Episodes Inference that minimizes the duplication episode depth. We prove that
this new variant of the problem can also be solved in polynomial time

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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: math
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The categories of this paper are: stat