Inferring a level-1 phylogenetic network from a dense set of rooted triplets
Theoretical Computer Science - Computing and combinatorics
Maximum agreement and compatible supertrees
Journal of Discrete Algorithms
A generalization of Haussler's convolution kernel: mapping kernel
Proceedings of the 25th international conference on Machine learning
Metrics for Phylogenetic Networks II: Nodal and Triplets Metrics
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Constructing Level-2 Phylogenetic Networks from Triplets
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
New results on optimizing rooted triplets consistency
Discrete Applied Mathematics
Fixed-Parameter Tractability of the Maximum Agreement Supertree Problem
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Constructing level-2 phylogenetic networks from triplets
RECOMB'08 Proceedings of the 12th annual international conference on Research in computational molecular biology
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)
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
The Complexity of Inferring A Minimally Resolved Phylogenetic Supertree
SIAM Journal on Computing
Fixed-Parameter algorithms for finding agreement supertrees
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
Fixed-parameter tractability of the maximum agreement supertree problem
CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching
Kernel and fast algorithm for dense triplet inconsistency
Theoretical Computer Science
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Given a set $\T$ of rooted, unordered trees, where each $T_i \in \T$ is distinctly leaf-labeled by a set $\Lambda(T_i)$ and where the sets $\Lambda(T_i)$ may overlap, the maximum agreement supertree problem~(MASP) is to construct a distinctly leaf-labeled tree $Q$ with leaf set $\Lambda(Q) \subseteq $\cup$_{T_i \in \T} \Lambda(T_i)$ such that $|\Lambda(Q)|$ is maximized and for each $T_i \in \T$, the topological restriction of $T_i$ to $\Lambda(Q)$ is isomorphic to the topological restriction of $Q$ to $\Lambda(T_i)$. Let $n = \left| $\cup$_{T_i \in \T} \Lambda(T_i)\right|$, $k = |\T|$, and $D = \max_{T_i \in \T}\{\deg(T_i)\}$. We first show that MASP with $k = 2$ can be solved in $O(\sqrt{D} n \log (2n/D))$ time, which is $O(n \log n)$ when $D = O(1)$ and $O(n^{1.5})$ when $D$ is unrestricted. We then present an algorithm for MASP with $D = 2$ whose running time is polynomial if $k = O(1)$. On the other hand, we prove that MASP is NP-hard for any fixed $k \geq 3$ when $D$ is unrestricted, and also NP-hard for any fixed $D \geq 2$ when $k$ is unrestricted even if each input tree is required to contain at most three leaves. Finally, we describe a polynomial-time $(n/\!\log n)$-approximation algorithm for MASP.