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A memory organization is considered for which a large number of faults can be tolerated at a low cost in redundancy. The primitive element in the memory is a large-scale integrated (LSI) chip that realizes a section of memory, b bits wide by y words long, together with an address decoder for the y words. The chips (including spares) are connected via a switching network so that the memory can be reconfigured effectively in the presence of chip failures. The main results of the paper relating to the switching network are as follows.