Regular Article: Extension Operations on Sets of Leaf-Labeled Trees
Advances in Applied Mathematics
SIAM Review
Journal of the ACM (JACM)
A few logs suffice to build (almost) all trees (l): part I
Random Structures & Algorithms
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
A supertree method for rooted trees
Discrete Applied Mathematics
WABI '02 Proceedings of the Second International Workshop on Algorithms in Bioinformatics
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
A linear-time heuristic for improving network partitions
DAC '82 Proceedings of the 19th Design Automation Conference
Using semi-definite programming to enhance supertree resolvability
WABI'05 Proceedings of the 5th International conference on Algorithms in Bioinformatics
Robustness of Topological Supertree Methods for Reconciling Dense Incompatible Data
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
New Perspectives on Gene Family Evolution: Losses in Reconciliation and a Link with Supertrees
RECOMB 2'09 Proceedings of the 13th Annual International Conference on Research in Computational Molecular Biology
New results on optimizing rooted triplets consistency
Discrete Applied Mathematics
Comparing and aggregating partially resolved trees
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Reconstructing approximate phylogenetic trees from quartet samples
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
The complexity of inferring a minimally resolved phylogenetic supertree
WABI'10 Proceedings of the 10th international conference on Algorithms in bioinformatics
Quartets MaxCut: A Divide and Conquer Quartets Algorithm
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
Comparing and aggregating partially resolved trees
Theoretical 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
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Supertree methods are used to construct a large tree over a large set of taxa from a set of small trees over overlapping subsets of the complete taxa set. Since accurate reconstruction methods are currently limited to a maximum of a few dozen taxa, the use of a supertree method in order to construct the tree of life is inevitable. Supertree methods are broadly divided according to the input trees: When the input trees are unrooted, the basic reconstruction unit is a quartet tree. In this case, the basic decision problem of whether there exists a tree that agrees with all quartets is NP-complete. On the other hand, when the input trees are rooted, the basic reconstruction unit is a rooted triplet and the above decision problem has a polynomial time algorithm. However, when there is no tree which agrees with all triplets, it would be desirable to find the tree that agrees with the maximum number of triplets. However, this optimization problem was shown to be NP-hard. Current heuristic approaches perform min cut on a graph representing the triplets inconsistency and return a tree that is guaranteed to satisfy some required properties. In this work, we present a different heuristic approach that guarantees the properties provided by the current methods and give experimental evidence that it significantly outperforms currently used methods. This method is based on a divide and conquer approach, where the min cut in the divide step is replaced by a max cut in a variant of the same graph. The latter is achieved by a lightweight semidefinite programming-like heuristic that leads to very fast running times.