# MPI-I-96-1-031

## On the complexity of computing evolutionary trees

### Gasieniec, Leszek and Jansson, Jesper and Lingas, Andrzej and Östlin, Anna

**MPI-I-96-1-031**. November** **1996, 14 pages. | Status:** **available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:

In this paper we study a few

important tree optimization problems with

applications to computational biology.

These problems ask for trees that are consistent with an

as large part of the given data as possible.

We show that the maximum homeomorphic agreement

subtree problem cannot be approximated within a factor of

$N^{\epsilon}$, where $N$ is the input size, for any $0 \leq \epsilon

< \frac{1}{18}$ in polynomial time, unless P=NP. On the other hand,

we present an $O(N\log N)$-time heuristic for the restriction of this

problem to instances with $O(1)$ trees of height $O(1)$,

yielding solutions within a constant factor of the optimum.

We prove that the maximum inferred consensus tree

problem is NP-complete and we provide a simple fast heuristic

for it, yielding solutions within one third of the optimum.

We also present a more specialized polynomial-time heuristic

for the maximum inferred local consensus tree problem.

Acknowledgement:** **

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**URL to this document: **http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1996-1-031

**BibTeX**
`@TECHREPORT{``GasieniecJanssonLingasÖstlin96``,`

` AUTHOR = {Gasieniec, Leszek and Jansson, Jesper and Lingas, Andrzej and {\"O}stlin, Anna},`

` TITLE = {On the complexity of computing evolutionary trees},`

` TYPE = {Research Report},`

` INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},`

` ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},`

` NUMBER = {MPI-I-96-1-031},`

` MONTH = {November},`

` YEAR = {1996},`

` ISSN = {0946-011X},`

`}`