 
Summary: 1
Approximate Maximum Parsimony
and Ancestral Maximum Likelihood
Noga Alon, Benny Chor, Fabio Pardi, Anat Rapoport
Abstract We explore the maximum parsimony (MP) and
ancestral maximum likelihood (AML) criteria in phyloge
netic tree reconstruction. Both problems are NP hard, so we
seek approximate solutions. We formulate the two problems
as Steiner tree problems under appropriate distances. The
gist of our approach is the succinct characterization of
Steiner trees for a small number of leaves for the two
distances. This enables the use of known Steiner tree
approximation algorithms. The approach leads to 16/9
approximation ratio for AML, and asymptotically to 1.55
approximation ratio for MP.
Index Terms Phylogenetic reconstruction, Ancestral
maximum likelihood, Maximum parsimony, Steiner trees,
Approximation algorithms.
I. INTRODUCTION
The ancestral maximum likelihood (AML) problem, also
