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Computational Complexity of Inferring Phylogenies by Compatibility

William H. E. Day and David Sankoff
Systematic Zoology
Vol. 35, No. 2 (Jun., 1986), pp. 224-229
DOI: 10.2307/2413432
Stable URL: http://www.jstor.org/stable/2413432
Page Count: 6
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Computational Complexity of Inferring Phylogenies by Compatibility
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Abstract

A well-known approach to inferring phylogenies involves finding a phylogeny with the largest number of characters that are perfectly compatible with it. Variations of this problem depend on whether characters are: cladistic (rooted) or qualitative (unrooted); binary (two states) or unconstrained (more than one state). The computational cost of known algorithms that guarantee solutions to these problems increases at least exponentially with problem size; practical computational considerations restrict the use of such algorithms to analyzing problems of small size. We establish that the four basic variants of the compatibility problem are all NP-complete and, thus, are so difficult computationally that for them efficient optimal algorithms are not likely to exist.

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