Two strategies are Used for the allocation of jobs to processors connected by mesh topologies: contiguous allocation and non-contiguous allocation. In noncontiguous allocation, a job request can be split into smaller parts that are allocated to non-adjacent free submeshes rather than always waiting until a single submesh of the requested size and shape is available. Lifting the contiguity condition is expected to reduce processor fragmentation and increase system utilization. However, the distances traversed by messages can be long, and as a result the communication overhead, especially contention, is increased. The extra communication overhead depends on how the allocation request is partitioned and assigned to free sub-meshes. This paper presents a new Noncontiguous allocation algorithm, referred to as GreedyAvailable-Busy-List (GABL for short), which can decrease the communication overhead among processors allocated to a given job. The simulation results show that the new strategy can reduce the communication overhead and substantially improve performance in terms of parameters such as job turnaround time and system utilization. Moreover, the results reveal that the ShortestService-Demand-First (SSD) scheduling strategy is much better than the First-Come-First-Served (FCFS) scheduling strategy.