A few logs suffice to build (almost) all trees: part II
Theoretical Computer Science
A few logs suffice to build (almost) all trees (l): part I
Random Structures & Algorithms
Multiple maxima of likelihood in phylogenetic trees: an analytic approach
RECOMB '00 Proceedings of the fourth annual international conference on Computational molecular biology
Inferring evolutionary trees with strong combinatorial evidence
Theoretical Computer Science - computing and combinatorics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Expander flows, geometric embeddings and graph partitioning
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Rec-I-DCM3: A Fast Algorithmic Technique for Reconstructing Large Phylogenetic Trees
CSB '04 Proceedings of the 2004 IEEE Computational Systems Bioinformatics Conference
Using Max Cut to Enhance Rooted Trees Consistency
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Distorted Metrics on Trees and Phylogenetic Forests
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Fast and reliable reconstruction of phylogenetic trees with very short edges
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Maximal accurate forests from distance matrices
RECOMB'06 Proceedings of the 10th annual international conference on Research in Computational Molecular Biology
An experimental study of quartets MaxCut and other supertree methods
WABI'10 Proceedings of the 10th international conference on Algorithms in bioinformatics
Comparing and aggregating partially resolved trees
Theoretical Computer Science
RECOMB'12 Proceedings of the 16th Annual international conference on Research in Computational Molecular Biology
A Linear Time Approximation Scheme for Maximum Quartet Consistency on Sparse Sampled Inputs
SIAM Journal on Discrete Mathematics
Qualitative organization of collections of shapes via quartet analysis
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
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Accurate phylogenetic reconstruction methods are currently limited to a maximum of few dozens of taxa. Supertree methods construct a large tree over a large set of taxa, from a set of small trees over overlapping subsets of the complete taxa set. Hence, in order to construct the tree of life over a million and a half different species, the use of a supertree method over the product of accurate methods, is inevitable. Perhaps the simplest version of this task that is still widely applicable, yet quite challenging, is quartet-based reconstruction. This problem lies at the root of many tree reconstruction methods and theoretical as well as experimental results have been reported. Nevertheless, dealing with false, conflicting quartet trees remains problematic. In this paper, we describe an algorithm for constructing a tree from a set of input quartet trees even with a significant fraction of errors. We show empirically that conflicts in the inputs are handled satisfactorily and that it significantly outperforms and outraces the Matrix Representation with Parsimony (MRP) methods that have previously been most successful in dealing with supertrees. Our algorithm is based on a divide and conquer algorithm where our divide step uses a semidefinite programming (SDP) formulation of MaxCut. We remark that this builds on previous work of ours [29] for piecing together trees from rooted triplet trees. The recursion for unrooted quartets, however, is more complicated in that even with completely consistent set of quartet trees the problem is NP-hard, as opposed to the problem for triples where there is a linear time algorithm. This complexity leads to several issues and some solutions of possible independent interest.