On mapping processes to processors in distributed systems
This paper is concerned with the implementation of parallel programs on networks of processors. In particular, we study the use of the network augmenting approach as an implementation tool. According to this approach, the capabilities of a given network of processors can be increased by adding some auxiliary links among the processors. We prove 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 a simple graph G is a set of vertex-disjoint paths that cover all the vertices of G and has the maximum possible number of edges. We present a linear time optimal path covering algorithm for a class of sparse graphs. This algorithm is of special interest since the optimal path covering problem is NP-complete for general graphs. Our results suggest that a ``cover and augment'' scheme can be used for optimal implementation of parallel programs in line-like networks.
scientific article; zbMATH DE number 4028885