  We develop a method for measuring homology classes. This involves three
problems. First, we define the size of a homology class, using ideas from
relative homology. Second, we define an optimal basis of a homology group to be
the basis whose elements' size have the minimal sum. We provide a greedy
algorithm to compute the optimal basis and measure classes in it. The algorithm
runs in $O(\beta^4 n^3 \log^2 n)$ time, where $n$ is the size of the simplicial
complex and $\beta$ is the Betti number of the homology group. Third, we
discuss different ways of localizing homology classes and prove some hardness
results.
