  The graph invariant EPT-sum has cropped up in several unrelated fields in
later years: As an objective function for hierarchical clustering, as a more
fine-grained version of the classical edge ranking problem, and, specifically
when the input is a vertex-weighted tree, as a measure of average/expected
search length in a partially ordered set. The EPT-sum of a graph $G$ is defined
as the minimum sum of the depth of every leaf in an edge partition tree (EPT),
a rooted tree where leaves correspond to vertices in $G$ and internal nodes
correspond to edges in $G$.
  A simple algorithm that approximates EPT-sum on trees is given by recursively
choosing the most balanced edge in the input tree $G$ to build an EPT of $G$.
Due to its fast runtime, this balanced cut algorithm can be used in practice,
and has earlier been analysed to give a 1.62-approximation on trees. In this
paper, we show that the balanced cut algorithm gives a 1.5-approximation of
EPT-sum on trees, which amounts to a tight analysis and answers a question
posed by Cicalese et al. in 2014.
