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Section: New Results

Keywords : Steiner minimum trees.

Computing Steiner minimum trees in Hamming metric (ATIPE)

Participant : Ernst Althaus.

In [22] we consider the problem of computing a Steiner minimum tree in Hamming metric. Given a set Im4 ${T\#8838 U}$ of required points (terminals) in an universe Uand a cost function Im5 ${c:U×U\#8614 \#8477 }$ , a Steiner tree is a tree connecting T$ \cup$S for a subset Im6 ${S\#8838 U}$ . A Steiner minimum tree Im7 ${{\mtext SMT}(T)}$ , is a Steiner tree of minimal cost.

The Steiner tree problem is one of the most studied NP-hard optimization problems (probably second after the Traveling Salesman problem). Here we are interested in the variant where Uis the set of strings of a certain length dand cis the Hamming distance between two strings.

The main application of this variant of the Steiner tree problem is to compute evolutionary trees in bioinformatics and computational linguistics.

Among all methods for finding such trees, algorithms using variations of a branch and bound method developed by Penny and Hendy have been the fastest for more than 20 years. We describe a new pruning approach that is far superior to previous methods and outline its implementation.


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