  We consider the problem of discretizing one-dimensional, real-valued
functions as graphs. The goal is to find a small set of points, from which we
can approximate the remaining function values. The method for approximating the
unknown values is interpolation on a discrete graph structure. From the
discrete graph structure, we build a refined approximation to the function over
its domain. This fine approximation can then be used for problems such as
optimization, which we illustrate by identifying local minima.
