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Processor allocation is done using space-sharing or time-sharing techniques. In timesharing techniques, processes are allocated to processors by dividing the time into separate slots, with each slot allocated to a different task. In space-sharing techniques processors are divided into physical partitions and once allocated, processes do not leave the system until they are completed and finished. Early processor allocation techniques were contiguous, in which the processors are constrained to be physically adjacent. These strategies suffered significantly from internal and external fragmentation. Non-contiguous processor allocation strategies have solved the fragmentation problem but have introduced a new problem called message-passing contention. In this article, we propose ESS, which is a new non-contiguous processor allocation strategy on mesh-connected parallel computers. ESS is noncontiguous, and gives a very compact allocation, and thus performs a very successful allocation with minimum contention. Furthermore, ESS is inherently parallelizable.