It is now more than a quarter of a century since researchers started publishing papers on mapping strategies for distributing computation across the computation resource of multiprocessor systems. There exists a large body of literature on the subject, but there is no commonly-accepted framework whereby results in the field can be compared. Nor is it always easy to assess the relevance of a new result to a particular problem. Furthermore, changes in parallel computing technology have made some of the earlier work of less relevance to current multiprocessor systems. Versions of the mapping problem are classified, and research in the field is considered in terms of its relevance to the problem of programming currently available hardware in the form of a distributed memory multiple instruction stream multiple data stream computer: a multicomputer.

In this paper we present discuss the task assignment problem for distributed systems. We also show how this problem is very similar to that of clustering transactions for load balancing purposes and for their efficient execution in a distributed environment. The formalization of these problems in terms of a graph theoretic representation of a distributed program, or of a set of related transactions, is given. The cost function which needs to be minimized by an assignment of tasks to processors or of transactions to clusters is detailed, and we survey related work, as well work on the dynamic load balancing problem. Since the task assignment problem is NP-hard, we present three novel heuristic algorithms that we have tested for solving it and compare them to the well-known greedy heuristic. These novel heuristics use neural networks, genetic algorithms and simulated annealing. Both the resulting performance and the computational cost for these algorithms is evaluated on a large number o...