On mapping processes to processors in distributed systems

The implementation of parallel programs on networks of processors is considered. Specifically, the use of the network augmenting approach as an implementation tool is examined. According to this approach, the capabilities of a given network of processors can be increased by adding some auxiliary connections among the processors. It is proved that the minimum set of edges needed to augment a line-like network so that it can accommodate a parallel program is determined by an optimal path cover of the graph representation of the program. An optimal path cover of a simple graph is a set of vertex-disjoint paths that cover all the vertices of that graph and has the maximum possible number of edges. A linear time optimal path covering algorithm for a class of sparse graphs is offered. This algorithm is of special interest because the optimal path covering problem is NP-complete for general graphs. The results indicate that a "cover and augment" scheme can be used for optimal implementation of parallel programs in line-like networks.