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
PY - 2003
Y1 - 2003
N2 - Maximum likelihood (ML) (Felsenstein, 1981) is an increasingly popular optimally 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.
AB - Maximum likelihood (ML) (Felsenstein, 1981) is an increasingly popular optimally 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.
UR - http://www.scopus.com/inward/record.url?scp=33645430074&partnerID=8YFLogxK
U2 - 10.1007/978-3-540-39763-2_16
DO - 10.1007/978-3-540-39763-2_16
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AN - SCOPUS:33645430074
SN - 0302-9743
VL - 2812
SP - 202
EP - 215
JO - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
JF - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ER -