Repeated computation of global functions in a distributed environment

In a distributed system, many algorithms need repeated computation of a global function. These algorithms generally use a static hierarchy for gathering the necessary data from all processes. As a result, they are unfair to processes at higher levels of the hierarchy, which have to perform more work than processes at lower levels do. 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 the 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 a distributed branch-and-bound problem and for asynchronous computation of fixed points