#### Date of Original Version

8-2012

#### Type

Conference Proceeding

#### Rights Management

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-642-32512-0_3

#### Abstract or Description

We study the problem of constructing phylogenetic trees for a given set of species. The problem is formulated as that of finding a minimum Steiner tree on *n* points over the Boolean hypercube of dimension *d*. It is known that an optimal tree can be found in linear time [1] if the given dataset has a perfect phylogeny, i.e. cost of the optimal phylogeny is exactly *d*. Moreover, if the data has a near-perfect phylogeny, i.e. the cost of the optimal Steiner tree is*d* + *q*, it is known [2] that an exact solution can be found in running time which is polynomial in the number of species and *d*, yet exponential in *q*. In this work, we give a polynomial-time algorithm (in both *d* and *q*) that finds a phylogenetic tree of cost *d* + *O*(*q* 2). This provides the best guarantees known—namely, a (1 + *o*(1))-approximation—for the case log(d)≪q≪d√, broadening the range of settings for which near-optimal solutions can be efficiently found. We also discuss the motivation and reasoning for studying such additive approximations.

#### DOI

10.1007/978-3-642-32512-0_3

#### Published In

Lecture Notes in Computer Science, 7408, 25-36.