A novel approach to phylogenetic trees: d-dimensional geometric Steiner trees ∗ Marcus Brazil † Benny K. Nielsen ‡ Doreen A. Thomas † Pawel Winter ‡ Christian Wulff-Nilsen ‡ Martin Zachariasen ‡ November 5, 2007 Abstract We suggest a novel distance-based method for the determination of phylogenetic trees. It is based on multidimensional scaling and Eu- clidean Steiner trees in high-dimensional spaces. Preliminary compu- tational experience shows that the use of Euclidean Steiner trees for finding phylogenetic trees is a viable approach. Experiments also in- dicate that the new method is comparable with results produced by Neighbor Joining [20]. Keywords: Phylogeny, Steiner tree, multidimensional scaling 1 Introduction One of the most important problems of modern biology is to explain how species have evolved over time and how they are related to each other. Such relationships are represented by phylogenetic trees where the leaf nodes rep- resent the species while the interior nodes represent their ancestors. Usu- ally, vertices of a phylogenetic tree represent sequences that identify the species, such as DNA or protein sequences, while edges represent changes (such as mutations, deletions and insertions) that have occurred to obtain one sequence from another. The major problem that faces biologists when constructing such phylogenetic trees is that the information about ancestors is very limited or is in fact non-existent. So the problem is to infer the * Partially supported by a grant from the Australia Research Council and by a grant from the Danish Natural Science Research Council (51-00-0336). † ARC Special Research Centre for Ultra-Broadband Information Networks (CUBIN) an affiliated program of National ICT Australia, Department of Electrical and Electronic Engineering, The University of Melbourne, Victoria 3010, Australia. E-mail: {brazil, d.thomas}@unimelb.edu.au. ‡ Department of Computer Science, University of Copenhagen, DK-2100 Copenhagen Ø, Denmark. E-mail: {benny, pawel, koolooz, martinz}@diku.dk. 1