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This paper presents parallel algorithms for computingmulti-dimensional wavelet transforms on both shared memory and distributedmemory machines. Traditional data partitioning methods for n-dimensionalDiscrete Wavelet Transforms (DWTs) call for data redistribution once a onedimensional wavelet transform is computed along each dimension. To avoid thedata communication inherent in this redistribution, two new partitioningmethods called CRBP (Communication Reduced BlockPartitioning) and CRLP (Communication Reduced LayerPartitioning) are proposed. The efficiency of the algorithms iscompared through several examples implemented on a cluster of SGIworkstations. Two kinds of parallel approaches are used to computemulti-dimensional wavelet transforms on shared memory machines: homogeneousparallelism, and heterogeneous parallelism. Homogeneous parallelism usestraditional data partitioning while heterogeneous parallelism uses the CRBPapproach. The effectiveness of these approaches is demonstrated throughseveral examples implemented on an SGI Power Challenge. The paper discussesthe effectiveness of each of the approaches on the two kinds ofarchitectures.