## Publications - Published papers

Please find below publications of our group. Currently, we list

**500**papers. Some of the publications are in collaboration with the group of Sonja Prohaska and are also listed in the publication list for her individual group. Access to published papers () is restricted to our local network and chosen collaborators. If you have problems accessing electronic information, please let us know:©NOTICE: All papers are copyrighted by the authors; If you would like to use all or a portion of any paper, please contact the author.

### Polynomial algorithms for the Maximal Pairing Problem: efficient phylogenetic targeting on arbitrary trees

*Christian Arnold, and Peter F. Stadler*

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#### Status:

Alg. Mol. Biol. 5: 25 (2010)

#### Abstract

<b>Background:</b>
The <em>Maximal Pairing Problem</em> (MPP) is the prototype of a class of combinatorial optimization problems that are of considerable interest in bioinformatics: Given an arbitrary phylogenetic tree <em>T</em> and weights <em>w<sub>xy</sub></em> for the paths between any two pairs of leaves <em>(x,y)</em>, what is the collection of edge-disjoint paths between pairs of leaves that maximizes the total weight? Special cases of the MPP for binary trees and equal weights have been described previously. Algorithms to solve the general MPP are still missing, however.<br>
<b>Results:</b>
We describe a relatively simple dynamic programming algorithm for the special case of binary trees. We then show that the general case of multifurcating trees can be treated by interleaving solutions to certain auxiliary Maximum Weighted Matching problems with an extension of this dynamic programming approach, resulting in an overall polynomial-time solution of complexity <em>O(n<sup>4</sup>log n)</em> w.r.t. the number <em>n</em> of leaves.
The source code of a C implementation can be obtained under the GNU Public License from
<tt>http://www.bioinf.uni-leipzig.de/Software/Targeting</tt>.
For binary trees, we furthermore discuss several constrained variants of the MPP as well as a partition function approach to the probabilistic version of the MPP. <br>
<b>Conclusions:</b>
The algorithms introduced here make it possible to solve the MPP also for large trees with high-degree vertices. This has practical relevance in the field of comparative phylogenetics and, for example, in the context of phylogenetic targeting, i.e., data collection with resource limitations.

#### Keywords

phylogenetic targeting, dynamics programming, maximum matching, combinatorial optimization