Some Approximation Results for the Maximum Agreement Forest Problem

Abstract

There are various techniques for reconstructing phylogenetic trees from data, and in this context the problem of determining how distant two such trees are from each other arises naturally. Various metrics (NNI, SPR, TBR) for measuring the distance between two phylogenies have been defined. Another way of comparing two trees $\mathcal{T}$ and $\mathcal{U}$ is to compute the so called maximum agreement forest of these trees. Informally, the number of components of an agreement forest tells how many edges need to be cut from each of $\mathcal{T}$ and $\mathcal{U}$ so that the resulting forests agree, after performing some forced edge contractions. This problem is known to be $\mathcal{N}\mathcal{P}$-hard. It was introduced by Hein et al. [3], who presented an approximation algorithm for it, claimed to have approximation ratio 3. We present here a 3-approximation algorithm for this problem and show that the performance ratio of Hein’s algorithm is 4.

This research is part of CAPES-COFECUB Project 272/99-II.

Supported by CNPq Grant Proc. 142307/97-1. Also supported by CAPES Grant BEX 0650-99/4 during her visit to Institut Pasteur, where part of this research was done.

Partially supported by CNPq (Procs. 304527/89-0 and 464114/00-4) and by ProNEx Project 107/97 (Proc. CNPq 664107/97-4).