If $K$ is a finite simplicial complex and $h$ is an injective map from the vertices of $K$ to $\R$, we show how to extend $h$ to a discrete Morse function in the sense of Forman in a reasonably efficient manner so that the resulting discrete Morse function mirrors the large-scale behavior of $h$. A concrete algorithm is given for the case where $K$ is a subcomplex of $\R^3$.
@article{1136926974,
author = {King, Henry and Knudson, Kevin and Mramor, Ne\v za},
title = {Generating Discrete Morse Functions from Point Data},
journal = {Experiment. Math.},
volume = {14},
number = {1},
year = {2005},
pages = { 435-444},
language = {en},
url = {http://dml.mathdoc.fr/item/1136926974}
}
King, Henry; Knudson, Kevin; Mramor, Neža. Generating Discrete Morse Functions from Point Data. Experiment. Math., Tome 14 (2005) no. 1, pp. 435-444. http://gdmltest.u-ga.fr/item/1136926974/