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Efficient processor allocation is crucial for obtaining high performance in space-shared parallel computers. A good processor allocation algorithm should find available processors for incoming jobs, if they exist, with minimum overhead. In this paper, we propose such a fast and efficient processor allocation scheme for mesh-connected multicomputers. By using simple coordinate calculation and spatial subtraction, the proposed scheme reduces the search space drastically and, hence, can locate a free submesh very quickly. The algorithm is implemented efficiently using a stack and therefore is called the stack-based allocation (SBA) algorithm. Extensive simulation reveals that our scheme incurs much less allocation overhead than all of the existing allocation algorithms, while delivering competitive performance.