Reconstruction of rooted trees from subtrees
Discrete Applied Mathematics
Determining the evolutionary tree using experiments
Journal of Algorithms
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A supertree method for rooted trees
Discrete Applied Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
WABI '02 Proceedings of the Second International Workshop on Algorithms in Bioinformatics
Rooted Maximum Agreement Supertrees
Algorithmica
SIAM Journal on Discrete Mathematics
Algorithms for Combining Rooted Triplets into a Galled Phylogenetic Network
SIAM Journal on Computing
Linear degree extractors and the inapproximability of max clique and chromatic number
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Algorithmic construction of sets for k-restrictions
ACM Transactions on Algorithms (TALG)
Using Max Cut to Enhance Rooted Trees Consistency
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Inferring a level-1 phylogenetic network from a dense set of rooted triplets
Theoretical Computer Science - Computing and combinatorics
Analytic solutions for three taxon ML trees with variable rates across sites
Discrete Applied Mathematics
Maximum agreement and compatible supertrees
Journal of Discrete Algorithms
Hardness of fully dense problems
Information and Computation
Journal of Discrete Algorithms
Constructing Level-2 Phylogenetic Networks from Triplets
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Computing a Smallest Multi-labeled Phylogenetic Tree from Rooted Triplets
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Fixed-parameter tractability of the maximum agreement supertree problem
CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching
Parameterized Complexity
The complexity of inferring a minimally resolved phylogenetic supertree
WABI'10 Proceedings of the 10th international conference on Algorithms in bioinformatics
Computing a Smallest Multilabeled Phylogenetic Tree from Rooted Triplets
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Conflict packing yields linear vertex-kernels for k-FAST, k-dense RTI and a related problem
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Comparing and aggregating partially resolved trees
Theoretical Computer Science
Complexity insights of the minimum duplication problem
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
The Complexity of Inferring A Minimally Resolved Phylogenetic Supertree
SIAM Journal on Computing
Kernel and fast algorithm for dense triplet inconsistency
Theoretical Computer Science
Gene tree correction for reconciliation and species tree inference: Complexity and algorithms
Journal of Discrete Algorithms
Hi-index | 0.06 |
A set of phylogenetic trees with overlapping leaf sets is consistent if it can be merged without conflicts into a supertree. In this paper, we study the polynomial-time approximability of two related optimization problems called the maximum rooted triplets consistency problem (MaxRTC) and the minimum rooted triplets inconsistency problem (MinRTI) in which the input is a set R of rooted triplets, and where the objectives are to find a largest cardinality subset of R which is consistent and a smallest cardinality subset of R whose removal from R results in a consistent set, respectively. We first show that a simple modification to Wu's Best-Pair-Merge-First heuristic Wu (2004) [38] results in a bottom-up-based 3-approximation algorithm for MaxRTC. We then demonstrate how any approximation algorithm for MinRTI could be used to approximate MaxRTC, and thus obtain the first polynomial-time approximation algorithm for MaxRTC with approximation ratio less than 3. Next, we prove that for a set of rooted triplets generated under a uniform random model, the maximum fraction of triplets which can be consistent with any phylogenetic tree is approximately one third. We then provide a deterministic construction of a triplet set having a similar property which is subsequently used to prove that both MaxRTC and MinRTI are NP-hard even if restricted to minimally dense instances. Finally, we prove that unless P=NP, MinRTI cannot be approximated within a ratio of c@?lnn for some constant c0 in polynomial time, where n denotes the cardinality of the leaf label set of R.