Recursive reconstruction on periodic trees
Random Structures & Algorithms
A few logs suffice to build (almost) all trees (l): part I
Random Structures & Algorithms
Efficient algorithms for inverting evolution
Journal of the ACM (JACM)
Glauber Dynamics onTrees and Hyperbolic Graphs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Fast mixing for independent sets, colorings and other models on trees
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
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
The Complexity of Distinguishing Markov Random Fields
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Reconstruction of Markov Random Fields from Samples: Some Observations and Algorithms
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Reconstruction for the Potts model
Proceedings of the forty-first annual ACM symposium on Theory of computing
Phylogenies without Branch Bounds: Contracting the Short, Pruning the Deep
RECOMB 2'09 Proceedings of the 13th Annual International Conference on Research in Computational Molecular Biology
Reconstructing approximate phylogenetic trees from quartet samples
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Reconstruction threshold for the hardcore model
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Topology discovery of sparse random graphs with few participants
Proceedings of the ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems
Topology discovery of sparse random graphs with few participants
ACM SIGMETRICS Performance Evaluation Review - Performance evaluation review
Learning Latent Tree Graphical Models
The Journal of Machine Learning Research
Phase transition for Glauber dynamics for independent sets on regular trees
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Alignment-Free phylogenetic reconstruction
RECOMB'10 Proceedings of the 14th Annual international conference on Research in Computational Molecular Biology
Fast and reliable reconstruction of phylogenetic trees with indistinguishable edges
Random Structures & Algorithms
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One of the major tasks of evolutionary biology is the reconstruction of phylogenetic trees from molecular data. The evolutionary model is given by a Markov chain on the true evolutionary tree. Given samples from this Markov chain at the leaves of the tree, the goal is to reconstruct the evolutionary tree.It is well known that in order to reconstruct a tree on n leaves, sequences of length Ω(log n) are needed. It was conjectured by M. Steel that for the CFN evolutionary model, if the mutation probability on all edges of the tree is less than p* = (√2-1)/23/2, then the tree can be recovered from sequences of length O(log n). This was proven by the second author in the special case where the tree is "balanced". The second author also proved that if all edges have mutation probability larger than p* then the length needed is nΩ(1). This "phase-transition" in the number of samples needed is closely related to the phase transition for the reconstruction problem (or extremality of free measure) studied extensively in statistical physics, probability and computer science.Here we complete the proof of Steel's conjecture and give a reconstruction algorithm using optimal (up to a multiplicative constant) sequence length. Our results further extend to obtain an optimal reconstruction algorithm for the Jukes-Cantor model with short edges. All reconstruction algorithms run in polynomial time.