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
Performance study of phylogenetic methods: (unweighted) quartet methods and neighbor-joining
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Orchestrating Quartets: Approximation and Data Correction
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Optimal phylogenetic reconstruction
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Using Max Cut to Enhance Rooted Trees Consistency
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
A linear time approximation scheme for maximum quartet consistency on sparse sampled inputs
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
A Linear Time Approximation Scheme for Maximum Quartet Consistency on Sparse Sampled Inputs
SIAM Journal on Discrete Mathematics
Phylogenetic tree reconstruction with protein linkage
ISBRA'12 Proceedings of the 8th international conference on Bioinformatics Research and Applications
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The reconstruction of evolutionary trees (also known as phylogenies) is central to many problems in Biology. Accurate phylogenetic reconstruction methods are currently limited to a maximum of few dozens of species. Therefore, in order to construct a tree over larger sets of species, a method capable of inferring accurately trees over small, overlapping sets, and subsequently merging these sets into a tree over the complete set, is required. A quartet tree is the smallest informative piece of information and quartet based methods are based on combining quartet trees into a big tree. However, even this case is NP-hard, and even when the set of quartet trees is compatible (agree on a certain tree). The general problem of approximating quartets, or maximum quartet consistency (MQC), even for compatible inputs, is open for nearly twenty years. Despite its importance, the only rigorous results for approximating quartets are the naive 1/3 approximation that applies to the general case and a PTAS when the input is the complete set of all (n4) possible quartets. Even when it is possible to determine the correct quartet induced by every four taxa, the time needed to generate the complete set of all quartets may be impractical. A faster approach is to sample at random just m ≪ (n4) quartets, and provide this sample as an input. In this work we present the first approximation algorithm whose guaranteed approximation is strictly better than 1/3 when the input is any random sample of m compatible quartets. The approximation ratio we obtain is 0.425 for general m, and 0.468 when m = w(n2). An important ingredient in our algorithm involves solving a weighted Max-Cut in a certain graph induced by the set of input quartets. We also show an extension of the PTAS algorithm to handle dense, rather than complete, inputs.