Near-Optimal Scheduling of Synchronous Data-Flow Graphs by Exact Calculation of Inter-Processor Communication Costs

Scheduling includes two major aspects: assigning tasks to processors and organising the data exchange between them. Many scheduling algorithms either neglect the costs for data exchange, consider them only for special topologies, or rely on worst case assumptions. Our aim was to optimise the mapping of synchronous data ow (SDF) graphs onto processor networks by coupling a universal routing algorithm with an appropriate scheduling strategy. For that purpose we chose the Dynamic Level Scheduling (DLS) algorithm 1]. The DLS algorithm assigns a dynamic level DL(v i ; p j) to each match between one task of the application represented by vertex v i of an acyclic directed graph and a processor p j. This parameter can be calculated by DL(v i ; p j) = X v2VL ExecutionTime(v) ? max(DA(v i ; p j); TF(p j)) (1) where V L denotes the set of vertices that make up the longest path from v i to an exit vertex, TF(p j) the earliest time, when processor p j becomes available, and DA(v i ; p j) the earliest time, when all input data for vertex v i are available at processor p j. The algorithm assigns v i to the processor p j that maximises DL. In (1) DA(v i ; p j) characterizes interprocessor communication cost and represents the earliest possible time to start the computation of v i with respect to communication. The common estimation which will be used as reference assumes that the diierence between DA(v i ; p j) and the time when all ancestor tasks of v i are nished is equal to the maximal product of the amount of data to be transferred and the number of hops between the two communicating processors. This approach will be compared to the exact calculation of interprocessor communication costs by software routing. Commonly used routing algorithms are tailored for a speciic topology. Instead of implementing a number of diierent algorithms, we developed a special routing algorithm capable of minimal routing in reconngurable communication networks 2]. A universal routing criterion is the minimisation of the remaining distance to the target processor for each routing step. The diierent network characteristics are coded in a suitable address scheme for each topology which reeects the connectivity of the network.