For execution of computation-intensive applications, one of the most important paradigms is to divide the application into a large number of small independent tasks and execute them on heterogeneous parallel computing environments (abbreviated by HPCEs). In this paper, we aim to execute independent tasks efficiently on HPCEs. We consider the problem to find a schedule that maximizes the throughput of task execution for a huge number of independent tasks. First, for HPCEs where the network forms a directed acyclic graph, we show that we can find, in polynomial time, a schedule that attains the optimal throughput. Secondly, for arbitrary HPCEs, we propose an (+ε)-approximation algorithm for any constant ε(ε>0). In addition, we also show that the framework of our approximation algorithm can be applied to other collective communications such as the gather operation.