Abstract: Segments or blocks of a file can be distributed among an number n of storage units by using a function of sequentially assigned segment identifiers for each segment, where the function is reduced modulo n, so long as the function is not congruent to segment identifier, modulo n, for any given segment identifier. An example of such a function, where n is the number of storage units and k is a segment identifier, is f(k)=ak+b, where a is relatively prime to n. Such a function can be computed quickly for any given segment. As the list of storage units changes, data may be redistributed using a new mapping of segments to storage units. Any new mapping can be restricted so that segments only move to a new storage unit or from an old storage unit, and not from one existing storage unit to another. In this way, the amount of data to be moved is limited. A chain of the lists of available storage units, as that list changes over time, is maintained to permit the history of file mappings to be recreated.