In a distributed system, many algorithms need repeated computation of
a global function. These algorithms generally use a static hierarchy
for gathering necessary data from all processes. As a result, they are
unfair to processes at higher levels of the hierarchy, who 
have to perform more work than processes at lower levels.
In this paper, we present a new revolving hierarchical scheme,
in which the position of a process in the hierarchy changes with time.
This reorganization of hierarchy
is achieved concurrently with its use. 
It results in algorithms that are
not only fair to all processes, but also less expensive in terms
of messages. The reduction in the number of messages is achieved 
by reusing messages for more than one computation of the global function.
The technique is illustrated 
for distributed branch-and-bound problem, and for asynchronous
computation of fixed points.