A conflict-free routing scheme on multistage interconnection networks

A conflict-free routing scheme is presented for a class of parallel and distributed computing systems. The core of the scheme is a quadtree communication structure. The quadtree structure suggests a general approach to mapping a class of parallel algorithms with intensive communication requirements for selecting data from many different sources and distributing data from a single source. By properly merging messages and efficiently replicating data, the quadtree structure can complete required communications in O(log₄ M) parallel steps, where M is the network size. It is shown that the size of a quadtree communication structure can be contracted and stretched by adjusting the number of descendent nodes without affecting its conflict-free property. The relationship between the computation/communication ratio of various parallel algorithms and the number of tree levels is presented, and finally, their joint effect on the response time of combining and distributing data messages is examined. This analysis helps determine the optimal adaptation of the quadtree for minimizing the overall algorithm execution time