1-optimality of static BSP computations: scheduling independent chains as a case study

The aim of this work is to study a specific scheduling problem under the machine-independent model BSP. The problem of scheduling a set of independent chains in this context is shown to be a difficult optimization problem, but it can be easily approximated in practice. Efficient heuristics taking into account communications are proposed and analyzed in this paper. We particularly focus on the influence of synchronization between consecutive supersteps. A family of algorithms is proposed with the best possible load-balancing. Then, a strategy for determining a good compromise between the two opposite criteria of minimizing the number of supersteps and a good balance of the load is derived. Finally, a heuristic which considers the influence of the latency is presented. Simulations of a large number of instances have been carried out to complement the theoretical worst case analysis. They confirm the very good behavior of the algorithms on the average cases.