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In non-contiguous allocation, a job request can be split into smaller parts that are allocated possibly non-adjacent free sub-meshes rather than always waiting until a single sub-mesh 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. In this paper, a new non-contiguous processor allocation strategy, referred to as A Compacting Non-Contiguous Processor Allocation Strategy (CNCPA), is suggested for the 2D mesh networks. In the proposed strategy, a single job is compacting into more than one free location within the allocated processors, where the remaining available processors (free processors) form a large sub-mesh in the system. To evaluate the performance improvement achieved by the proposed strategy and compare it against well-known existing non-contiguous allocation strategies, we conduct extensive simulation experiments under the assumption of wormhole routing and the one-to-all and near neighbor communication patterns. The results show that the proposed strategy can eliminate both the internal and external fragmentation and reduce the communication overhead and hence improve performance in terms of job turnaround time and system utilization.