Optimum divisible load scheduling on heterogeneous stars with limited memory

Scheduling divisible application on a set of heterogeneous processors with limited memory sizes is analyzed in this paper. Divisible loads are computations which allow for dividing computations into several parts of arbitrary sizes, and the parts can be processed independently in parallel. Though the model originated in the parallel computing context, it has strong links with other applications of operations research. A star communication network is assumed. Each processing element of the network is characterized by the processing speed, memory size, speed and startup time of its communication link. The goal is to find a distribution of the load whose schedule length is minimum. The problem is established to be computationally hard. Therefore, two types of algorithms are proposed, and evaluated: an exact algorithm whose execution time may be exponential, and polynomial-time heuristics.