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Service level agreements (SLAs) are currently one of the major research topics in Grid Computing. Among many system components for supporting of SLA-aware Grid-based workflows, the SLA mapping module receives an important position. Mapping light communication workflows is one main part of the mapping module. With the previously proposed mapping algorithm, the mapping module may become the bottleneck of the system when many requests come in a short period of time. This paper presents a parallel mapping algorithm for light communication SLA-based workflows, which can cope with the problem. Performance measurements deliver evaluation results on the quality of the method.