To minimize the execution time of a parallel application running on a heterogeneous computing distributed system, an appropriate mapping scheme to allocate the application tasks to the processors is needed. The general problem of mapping tasks to machines is a well known NP-hard problem and several heuristics have been proposed to approximate its optimal solution. In this paper we propose a static graph-based mapping algorithm, called Heterogeneous Multi-phase Mapping (HMM), that permits a suboptimal mapping of a parallel application onto a heterogeneous computing distributed system by using a local search technique together with a tabu search meta-heuristic. HMM allocates parallel tasks by exploiting the information embedded in the parallelism forms used to implement an application. We compare HMM with three different leading techniques and with an exhaustive mapping algorithm. We also give an example of mapping of a pratical application where HMM verified its usefulness. Experimental results show that HMM performs well demonstrating the applicability of our approach.
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