  Calculating and categorizing the similarity of curves is a fundamental
problem which has generated much recent interest. However, to date there are no
implementations of these algorithms for curves on surfaces with provable
guarantees on the quality of the measure. In this paper, we present a
similarity measure for any two cycles that are homologous, where we calculate
the minimum area of any homology (or connected bounding chain) between the two
cycles. The minimum area homology exists for broader classes of cycles than
previous measures which are based on homotopy. It is also much easier to
compute than previously defined measures, yielding an efficient implementation
that is based on linear algebra tools. We demonstrate our algorithm on a range
of inputs, showing examples which highlight the feasibility of this similarity
measure.
