The maximum rooted resolved triplets consistency problem takes as input a set R of resolved triplets and asks for a rooted phylogenetic tree that is consistent with the maximum number of elements in R. This paper studies the polynomial-time approximability of a generalization of the problem where in addition to resolved triplets, the input may contain fan triplets and forbidden triplets. To begin with, we observe that the generalized problem admits a 1/4-approximation in polynomial time. Next, we present a polynomial-time approximation scheme (PTAS) for dense instances based on smooth polynomial integer programming. Finally, we generalize Wu’s exact exponential-time algorithm in [19] for the original problem to also allow fan triplets, forbidden resolved triplets, and forbidden fan triplets. Forcing the algorithm to always output a k-ary phylogenetic tree for any specified k ≥ 2 then leads to an exponential-time approximation scheme (ETAS) for the generalized, unrestricted problem.
CITATION STYLE
Jansson, J., Lingas, A., & Lundell, E. M. (2015). The approximability of maximum rooted triplets consistency with fan triplets and forbidden triplets. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9133, pp. 272–283). Springer Verlag. https://doi.org/10.1007/978-3-319-19929-0_23
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