  Given a simplicial complex $K$ and an injective function $f$ from the
vertices of $K$ to $\mathbb{R}$, we consider algorithms that extend $f$ to a
discrete Morse function on $K$. We show that an algorithm of King, Knudson and
Mramor can be described on the directed Hasse diagram of $K$. Our description
has a faster runtime for high dimensional data with no increase in space.
