Computing a Smallest Multi-labeled Phylogenetic Tree from Rooted Triplets
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
RECOMB-CG'10 Proceedings of the 2010 international conference on Comparative genomics
Clustering with relative constraints
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
Kernel and fast algorithm for dense triplet inconsistency
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
| Hi-index | 0.00 |
A set of phylogenetic trees with overlapping leaf sets isconsistent if it can be merged without conflicts into a supertree.In this paper, we study the polynomial-time approximability of tworelated optimization problems called the maximum rooted tripletsconsistency problem ($\textsc{MaxRTC}$) and the minimum rootedtriplets inconsistency problem ($\textsc{MinRTI}$) in which theinput is a set $\mathcal{R}$ of rooted triplets, and where theobjectives are to find a largest cardinality subset of$\mathcal{R}$ which is consistent and a smallest cardinality subsetof $\mathcal{R}$ whose removal from $\mathcal{R}$ results in aconsistent set, respectively. We first show that a simplemodification to Wu’s Best-Pair-Merge-First heuristic [25]results in a bottom-up-based 3-approximation for $\textsc{MaxRTC}$.We then demonstrate how any approximation algorithm for$\textsc{MinRTI}$ could be used to approximate $\textsc{MaxRTC}$,and thus obtain the first polynomial-time approximation algorithmfor $\textsc{MaxRTC}$ with approximation ratio smaller than 3.Next, we prove that for a set of rooted triplets generated under auniform random model, the maximum fraction of triplets which can beconsistent with any tree is approximately one third, and thenprovide a deterministic construction of a triplet set having asimilar property which is subsequently used to prove that both$\textsc{MaxRTC}$ and $\textsc{MinRTI}$ are NP-hard even ifrestricted to minimally dense instances. Finally, we prove that$\textsc{MinRTI}$ cannot be approximated within a ratio ofΩ(logn) in polynomial time, unless P = NP.