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.

A heterogeneous parallel computing environment consisting of different types of workstations and communication links plays an important role in parallel computing. In many applications on the system, collective communication operations are commonly used as communication primitives. Thus, design of the efficient collective communication operations is the key to achieve high-performance parallel computing. But the heterogeneity of the system complicates the design. In this paper, we consider design of an efficient gather operation, one of the most important collective operations. We show that an optimal gather schedule is found in O(n2k-1) time for the heterogeneous parallel computing environment with n processors of k distinct types, and that a nearly-optimal schedule is found in O(n) time if k=2.