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Distributed computing systems are a viable and less expensive alternative to parallel computers. However, a serious difficulty in concurrent programming of a distributed system is how to deal with scheduling and load balancing of such a system which may consist of heterogeneous computers. Loop scheduling schemes for parallel computers and computer clusters have been proposed in the past. All these schemes are one-dimensional because they partition only the outermost loop of a nested loop construct. In this work, we consider scheduling nested loops with many dimensions. We propose a new methodology which partitions many levels (or dimensions) of nested loops. These new schemes show superior performance over the existing schemes. We implement our new schemes on a network of computers and make performance comparisons with other existing schemes. We expect the new schemes to be particularly useful for multi-core systems because of the fine granularity of the generated tasks.