  The general communication tree embedding problem is the problem of mapping a
set of communicating terminals, represented by a graph G, into the set of
vertices of some physical network represented by a tree T. In the case where
the vertices of G are mapped into the leaves of the host tree T the underlying
tree is called a routing tree and if the internal vertices of T are forced to
have degree 3, the host tree is known as layout tree. Different optimization
problems have been studied in the class of communication tree problems such as
well-known minimum edge dilation and minimum edge congestion problems. In this
report we study the less investigate measure i.e. tree length, which is a
representative for average edge dilation (communication delay) measure and also
for average edge congestion measure. We show that finding a routing tree T for
an arbitrary graph G with minimum tree length is an NP-Hard problem.
