Shared Memory Processors (SMP) workstation clusters are becoming more and more popular. To optimize communication between the workstations, a new graph partition problem was developed to schedule tasks in SMP clusters. The problem is NP-complete and a heuristic algorithm was developed based on Lee, Kim and Park’s algorithm. Experimental results indicate that our algorithm outperforms theirs, especially when the number of partitions is large. This algorithm can be integrated in a parallelizing compiler as a back end optimizer for the distributed code generator.