We propose a most economical design of the Optical Shared MemOry Supercomputer Interconnect System (OSMOSIS) all-optical, wavelength-space crossbar switch fabric. It is shown, by analysis and simulation, that the total number of on-off gates required for the proposed N × N switch fabric can scale asymptotically as N ln N if the number of input/output ports N can be factored into a product of small primes. This is of the same order of magnitude as Shannon's lower bound for switch complexity, according to which the minimum number of two-state switches required for the construction of a N × N permutation switch is log2 (N!).