Maximum savings in the Steiner problem in phylogeny

Abstract

The problem of constructing a phylogeny (evolutionary tree) from a given set of protein sequences is discussed. It is shown to be a special case of the Steiner problem in graphs, called the Steiner problem in phylogeny. A question which arises naturally is what is the maximum fraction ρ say, by which the length of any minimal spanning tree solution can be reduced by the introduction of Steiner points? In this note we show that asymptotically, ρ = 1/2. We furnish a numerical example which shows that this bound is sharp.