Abstract. This paper presents new techniques for master-slave tasking on treeshaped networks with fully heterogeneous communication and processing resources. A large number of independent, equal-sized tasks are distributed from the master node to the slave nodes for processing and return of result files. The network links present bandwidth asymmetry, i.e. the send and receive bandwidths of a link may be different. The nodes can overlap computation with at most one send and one receive operation. A centralized algorithm that maximizes the platform throughput under static conditions is presented. Thereafter, we propose several distributed heuristics making scheduling decisions based on information estimated locally. Extensive simulations demonstrate that distributed heuristics are better suited to cope with dynamic environments, but also compete well with centralized heuristics in static environments.