Unique perfect phylogeny is intractable

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Unique perfect phylogeny is intractable

A phylogeny is a tree capturing evolution and ancestral relationships of a set of taxa (e.g., species). Reconstructing phylogenies from molecular data plays an important role in many areas of contemporary biological research. A phylogeny is perfect if (in rough terms) it correctly captures all input data. Determining if a perfect phylogeny exists was shown to be intractable in 1992 by Mike Stee...

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Unique Perfect Phylogeny Is NP-Hard

We answer, in the affirmitive, the following question proposed by Mike Steel as a $100 challenge: “Is the following problem NP hard? Given a ternary phylogenetic X-tree T and a collection Q of quartet subtrees on X, is T the only tree that displays Q?” [25,27]

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The perfect phylogeny problem is a classic problem in computational biology, where we seek an unrooted phylogeny that is compatible with a set of qualitative characters. Such a tree exists precisely when an intersection graph associated with the character set, called the partition intersection graph, can be triangulated using a restricted set of fill edges. Semple and Steel used the partition i...

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Haplotyping is the bioinformatics problem of predicting likely haplotypes based on given genotypes. It can be approached using Gusfield’s perfect phylogeny haplotyping (PPH) method for which polynomial and linear time algorithms exist. These algorithm use sophisticated data structures or do a stepwise transformation of the genotype data into haplotype data and, therefore, need a linear amount o...

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Perfect phylogeny is one of the fundamental models for studying evolution. We investigate the following variant of the problem: The input is an n ×m species-characters matrix. The characters are binary and directed, i.e., a species can only gain characters. The difference from standard perfect phylogeny is that for some species the state of some characters is unknown. The question is whether on...

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ژورنال

عنوان ژورنال: Theoretical Computer Science

سال: 2013

ISSN: 0304-3975

DOI: 10.1016/j.tcs.2012.12.048