TY - JOUR

T1 - Ancestral maximum likelihood of evolutionary trees is hard

AU - Addario-Berry, Louigi

AU - Chor, Benny

AU - Hallett, Mike

AU - Lagergren, Jens

AU - Panconesi, Alessandro

AU - Wareham, Todd

N1 - Funding Information:
We would like to thank the staff of the Bellairs Research Institute of McGill University, where much of the research reported here was done, for their hospitality. The research reported here was supported by ISF grant 418/00 (BC), the EU thematic network APPOL (AP), and NSERC grant 228104 (TW).

PY - 2004/6

Y1 - 2004/6

N2 - Maximum likelihood (ML) (Neyman, 1971) is an increasingly popular optimality criterion or 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.

AB - Maximum likelihood (ML) (Neyman, 1971) is an increasingly popular optimality criterion or 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.

KW - Computational complexity

KW - Maximum likelihood

KW - Phylogeny inference

UR - http://www.scopus.com/inward/record.url?scp=4043184290&partnerID=8YFLogxK

U2 - 10.1142/S0219720004000557

DO - 10.1142/S0219720004000557

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AN - SCOPUS:4043184290

SN - 0219-7200

VL - 2

SP - 257

EP - 271

JO - Journal of Bioinformatics and Computational Biology

JF - Journal of Bioinformatics and Computational Biology

IS - 2

ER -