Finding a maximum likelihood tree is hard

Abstract. 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 [Foulds and Graham, 1982; Day et al. 1986], 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 the parsimony values of given sequences and the corresponding log likelihood values. However, a direct application of their work 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 ancestra...

• Type: Journal
• Year: 2006
• Where: JACM
• Authors: Benny Chor, Tamir Tuller
• Keywords: Addario-Berry Et Al, Et Al, JACM 2006, Maximum Likelihood