Ancestral Maximum Likelihood of Evolutionary Trees Is Hard

  • Louigi Addario-Berry
  • Benny Chor
  • Mike Hallett
  • Jens Lagergren
  • Alessandro Panconesi
  • Todd Wareham
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2812)


Maximum likelihood (ML) (Felsenstein, 1981) is an increasingly popular optimality criterion for selecting evolutionary trees. Finding optimal ML trees appears to be a very hard computational task – in particular, algorithms and heuristics for ML take longer to run than algorithms and heuristics for maximum parsimony (MP). However, while MP has been known to be NP-complete for over 20 years, no such hardness result has been obtained so far for ML.

In this work we make a first step in this direction by proving that ancestral maximum likelihood (AML) is NP-complete. The input to this problem is a set of aligned sequences of equal length and the goal is to find a tree and an assignment of ancestral sequences for all of that tree’s internal vertices such that the likelihood of generating both the ancestral and contemporary sequences is maximized. Our NP-hardness proof follows that for MP given in (Day, Johnson and Sankoff, 1986) in that we use the same reduction from Vertex Cover; however, the proof of correctness for this reduction relative to AML is different and substantially more involved.


Maximum Parsimony Evolutionary Tree Vertex Cover Internal Vertex Ancestral Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Louigi Addario-Berry
    • 1
  • Benny Chor
    • 2
  • Mike Hallett
    • 1
  • Jens Lagergren
    • 3
  • Alessandro Panconesi
    • 4
  • Todd Wareham
    • 5
  1. 1.McGill Centre for Bioinformatics, School of Computer ScienceMcGill UniversityMontrealCanada
  2. 2.School of Computer ScienceTel-Aviv UniversityIsrael
  3. 3.Stockholm Bioinformatics Center and, Department of Numerical Analysis and Computer ScienceKTHStockholmSweden
  4. 4.Dipartimento di InformaticaUniversitá di Roma “La Sapienza”RomeItaly
  5. 5.Department of Computer ScienceMemorial University of NewfoundlandSt. John’sCanada

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