Service Level Agreements (SLAs) are currently one of the major research topics in Grid Computing. Among those system components that support SLA-aware Grid jobs, the SLA mapping mechanism has an important position. It is responsible for assigning sub-jobs of the workflow to Grid resources in a way that meets the user's deadline and minimizes costs. Assuming many different kinds of sub-jobs and resources, the process of mapping an SLA-based workflow with light communication defines an unfamiliar and difficult problem. This paper presents a solution to this problem. The quality and efficiency of the algorithm is validated through performance measurements.