I
NSTANCE
:
A 3-degree (binary) tree
with unique labels on the leaves
and with edge weights
. A 3-degree tree
T'
with the
same set of unique labels as
T
.
S
OLUTION
:
A sequence of edges
representing nearest neighbour
interchanges transforming the tree
T
into
T'
(so that the labels match).
A nearest neighbour interchange of
is a transformation where
one of the two subtrees adjacent to
u
is exchanged with one of the two
subtrees adjacent to
v
.
M
EASURE
:
The cost of the sequence of interchanges, i.e.,
.
Good News:
Approximable within
where
n
is the number of leaves
[
91
].
Comment:
The variation when another type of transformation called
linear-cost
subtree transfer
is used is approximable within 2
[
91
].