This article compares three techniques for allocating tasks in a mesh-based multi-computer. Tasks are expressed as rectangles of a certain width and height corresponding to the topology of processors desired. The task allocation problem, is thus a variant of the bin-packing problem, with one major difference: in the bin-packing problem one seeks to minimize the height of the bin, while here we seek to maximize the utilization of processors in a multicomputer. The three techniques compared are a classical level-by-level algorithm, a connectionist simulated annealing variant of the Hopfield network, and a genetic algorithm. An extension to the dynamic processor allocation problem is modeled by fixing some rectangles in place and packing the request rectangles in the residual space on the mesh; this corresponds to a pre-existing condition, i.e., some tasks have already been allocated to the Processor Mesh. Implementation and experimental results are presented.
Approximation Schemes for the Generalized Extensible Bin Packing Problem
