Efficient Coarse Grained Data Distributions and String Pattern Matching

Distributing a packet of data from a source processor to all processors in a parallel computer is a fundamental operation. The efficiency of this operation depends on the configuration of the processors. We show that the sets of architectures A allowing efficient distribution for coarse grained multicomputers include those satisfying the hypothesis that there exists a constant cA such that every member of A has a spanning tree in which all vertices have degree less than cA. We give a simple example of a set A that does not satisfy this hypothesis and whose members cannot distribute a packet of data efficiently. We discuss applications of this result to string pattern recognition