  Erling Folner proved that the amenability or nonamenability of a countable
group depends on the complexity of its finite subsets. Complexity has three
measures: maximum Folner ratio, optimal cooling function, and minimum cooling
norm. Our first aim is to show that, for a fixed finite subset, these three
measures are tightly bound to one another. We then explore their algorithmic
calculation. Our intent is to provide a theoretical background for
algorithmically exploring the amenability and nonamenability of discrete
groups.
