Randomized algorithms
Some optimal inapproximability results
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Algorithms for Combining Rooted Triplets into a Galled Phylogenetic Network
SIAM Journal on Computing
Inferring a level-1 phylogenetic network from a dense set of rooted triplets
Theoretical Computer Science - Computing and combinatorics
The Structure of Level-k Phylogenetic Networks
CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
New results on optimizing rooted triplets consistency
Discrete Applied Mathematics
Asymptotic limits of a new type of maximization recurrence with an application to bioinformatics
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
| Hi-index | 0.00 |
The study of phylogenetic networks is of great interest to computational evolutionary biology and numerous different types of such structures are known. This article addresses the following question concerning rooted versions of phylogenetic networks. What is the maximum value of p@?[0,1] such that for every input set T of rooted triplets, there exists some network N such that at least p|T| of the triplets are consistent with N? We call an algorithm that computes such a network (where p is maximum) worst-case optimal. Here we prove that the set containing all triplets (the full triplet set) in some sense defines p. Moreover, given a network N that obtains a fraction p^' for the full triplet set (for any p^'), we show how to efficiently modify N to obtain a fraction =p^' for any given triplet set T. We demonstrate the power of this insight by presenting a worst-case optimal result for level-1 phylogenetic networks improving considerably upon the 5/12 fraction obtained recently by Jansson, Nguyen and Sung. For level-2 phylogenetic networks we show that p=0.61. We emphasize that, because we are taking |T| as a (trivial) upper bound on the size of an optimal solution for each specific input T, the results in this article do not exclude the existence of approximation algorithms that achieve approximation ratio better than p. Finally, we note that all the results in this article also apply to weighted triplet sets.