On Some Tighter Inapproximability Results (Extended Abstract)
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
A Short Proof that Phylogenetic Tree Reconstruction by Maximum Likelihood Is Hard
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)
The gene evolution model and computing its associated probabilities
Journal of the ACM (JACM)
An open source phylogenetic search and alignment package
International Journal of Bioinformatics Research and Applications
Visualizing phylogenetic treespace using cartographic projections
WABI'09 Proceedings of the 9th international conference on Algorithms in bioinformatics
Phylogenetic models of rate heterogeneity: a high performance computing perspective
IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
Likely scenarios of intron evolution
RCG'05 Proceedings of the 2005 international conference on Comparative Genomics
An improved algorithm for the macro-evolutionary phylogeny problem
CPM'06 Proceedings of the 17th Annual conference on Combinatorial Pattern Matching
Parallel divide-and-conquer phylogeny reconstruction by maximum likelihood
HPCC'05 Proceedings of the First international conference on High Performance Computing and Communications
Using semi-definite programming to enhance supertree resolvability
WABI'05 Proceedings of the 5th International conference on Algorithms in Bioinformatics
A hybrid micro-macroevolutionary approach to gene tree reconstruction
RECOMB'05 Proceedings of the 9th Annual international conference on Research in Computational Molecular Biology
Proceedings of the 20th European MPI Users' Group Meeting
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Maximum likelihood (ML) is an increasingly popular optimality criterion for selecting evolutionary trees (Felsenstein, 1981). Finding optimal ML trees appears to be a very hard computational task, but for tractable cases, ML is the method of choice. In particular, algorithms and heuristics for ML take longer to run than algorithms and heuristics for the second major character based criterion, maximum parsimony (MP). However, while MP has been known to be NP-complete for over 20 years (Day, Johnson and Sankoff [5], reduction from vertex cover), such a hardness result for ML has so far eluded researchers in the field. An important work by Tuffley and Steel (1997) proves quantitative relations between parsimony values and the corresponding log likelihood values. However, a direct application of it would only give an exponential time reduction from MP to ML. Another step in this direction has recently been made by Addario-Berry et al. (2004), who proved that ancestral maximum likelihood (AML) is NP-complete. AML “lies in between” the two problems, having some properties of MP and some properties of ML. We resolve the question, showing that “regular” ML on phylogenetic trees is indeed intractable. Our reduction follows those for MP and AML, but starts from an approximation version of vertex cover, known as gap vc. The crux of our work is not the reduction, but its correctness proof. The proof goes through a series of tree modifications, while controlling the likelihood losses at each step, using the bounds of Tuffley and Steel. The proof can be viewed as correlating the value of any ML solution to an arbitrarily close approximation to vertex cover.