This work addresses the problem of allocating parallel application tasks to heterogeneous distributed computing resources, such as multiclusters or Grid environments. The proposed allocation scheme is based on a multilevel graph partitioning and mapping approach. The objective is to find an efficient allocation that minimizes the application completion time, subject to the specified constraints pertinent to the application and system environment. The allocation scheme consists of three phases; the clustering phase, the initial mapping phase and the refinement and remapping phase. The scheme introduces an efficient heuristic in the clustering phase for contracting (coarsening) large size application graphs to the number of processors, called the VHEM method. An initial mapping technique based on a tabu-search approach has been introduced as a basis for the process of refinement and remapping phase. The simulation study shows that the VHEM coarsening heuristic can achieve optimal or near-optimal communication, compared to the HEM method, when the ratio of the number of tasks to the number of processors exceeds a threshold value. The simulation study shows that those optimal or near-optimal VHEM-coarsened graphs have an effect of generating very efficient mappings, when they are compared to the HEM-coarsened graphs.
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