Alignment-free phylogenetic reconstruction: Sample complexity via a   branching process analysis
  We present an efficient phylogenetic reconstruction algorithm allowing insertions and deletions which provably achieves a sequence-length requirement (or sample complexity) growing polynomially in the number of taxa. Our algorithm is distance-based, that is, it relies on pairwise sequence comparisons. More importantly, our approach largely bypasses the difficult problem of multiple sequence alignment. 
Constantinos Daskalakis, Sebastien Roch
math.PR cs.CE cs.DS math.ST q-bio.PE stat.TH