Abstract: During the last years, the genomes of more and more
species have been sequenced, providing data for phylogenetic recon-
struction based on genome rearrangement measures. A main task in
all phylogenetic reconstruction algorithms is to solve the median of
three problem. Although this problem is NP-hard even for the sim-
plest distance measures, there are exact algorithms for the breakpoint
median and the reversal median that are fast enough for practical use.
In this paper, this approach is extended to the transposition median as
well as to the weighted reversal and transposition median. Although
there is no exact polynomial algorithm known even for the pairwise
distances, we will show that it is in most cases possible to solve
these problems exactly within reasonable time by using a branch and
bound algorithm.