We study the problem of constructing phylogenetic trees for a given set of species. The problem is formulated as that of finding a minimum Steiner tree on n points over the Boolean hypercube of dimension d. It is known that an optimal tree can be found in linear time [1] if the given dataset has a perfect phylogeny, i.e. cost of the optimal phylogeny is exactly d. Moreover, if the data has a near-perfect phylogeny, i.e. the cost of the optimal Steiner tree is d + q, it is known [2] that an exact solution can be found in running time which is polynomial in the number of species and d, yet exponential in q. In this work, we give a polynomial-time algorithm (in both d and q) that finds a phylogenetic tree of cost d + O(q 2). This provides the best guarantees known-namely, a (1 + o(1))-approximation-for the case log(d) ≪ q ≪ √d, broadening the range of settings for which near-optimal solutions can be efficiently found. We also discuss the motivation and reasoning for studying such additive approximations. © 2012 Springer-Verlag.
CITATION STYLE
Awasthi, P., Blum, A., Morgenstern, J., & Sheffet, O. (2012). Additive approximation for near-perfect phylogeny construction. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7408 LNCS, pp. 25–36). https://doi.org/10.1007/978-3-642-32512-0_3
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