Abstract
The maximum rooted resolved triplets consistency problem takes as input a set \(\mathcal {R}\) of resolved triplets and asks for a rooted phylogenetic tree that is consistent with the maximum number of elements in \(\mathcal {R}\). 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 \(k \ge 2\) then leads to an exponential-time approximation scheme (ETAS) for the generalized, unrestricted problem.
JJ was funded by The Hakubi Project and KAKENHI grant number 26330014.
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Jansson, J., Lingas, A., Lundell, EM. (2015). The Approximability of Maximum Rooted Triplets Consistency with Fan Triplets and Forbidden Triplets. In: Cicalese, F., Porat, E., Vaccaro, U. (eds) Combinatorial Pattern Matching. CPM 2015. Lecture Notes in Computer Science(), vol 9133. Springer, Cham. https://doi.org/10.1007/978-3-319-19929-0_23
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