Regular Article: Extension Operations on Sets of Leaf-Labeled Trees
Advances in Applied Mathematics
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
Expander flows, geometric embeddings and graph partitioning
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Convex recolorings of strings and trees: Definitions, hardness results and algorithms
Journal of Computer and System Sciences
Maximum likelihood of evolutionary trees is hard
RECOMB'05 Proceedings of the 9th Annual international conference on Research in Computational Molecular Biology
Using Max Cut to Enhance Rooted Trees Consistency
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
A Heuristic for Fair Correlation-Aware Resource Placement
SEA '09 Proceedings of the 8th International Symposium on Experimental Algorithms
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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 few dozens of 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 mincut 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 divide and conquer where we use a semi-definite programming approach in the divide step.