Efficient allocation of processors to incoming tasks in parallel computer systems is very important for achieving the desired high performance. It requires recognizing the free available processors with minimum overhead. In this paper, we present an efficient task allocation scheme for 2D mesh architectures. By employing a new approach for searching the mesh, our scheme can find the available submesh without scanning the entire mesh, unlike earlier designs. Comprehensive computer simulation reveals that the average allocation time and waiting delay are much smaller than earlier schemes of comparable performances, irrespective of the size of meshes and distribution of the shape of the incoming tasks.
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