In this example, we could calculate the change in the effective energy locally, i.e., by visiting the neighbors of the target of the index copy. Most effective energies are quasi-local, allowing calculations of similar to those presented above. The locality of the effective energy is crucial to the utility of the GGH approach. If we had to calculate the effective energy for the entire cell lattice for each index-copy attempt, the algorithm would be prohibitively slow.
and 
denote the volumes of the generalized cells containing 
similar to those presented above. The locality of the effective energy is crucial to the utility of the GGH approach. If we had to calculate the effective energy for the entire cell lattice