Embedding arbitrary trees in the hypercube and the q-dimensional mesh

A general data movement technique was described by D. Nassimi and S. Sahni (1981) which often leads to efficient parallel algorithms on distributed-memory architectures for a wide class of problems. In this paper, by using the same arguments that was used to prove correctness of this technique, we show that the data movement operations involved may be reduced by a constant factor under some assumptions. We show also that this technique and the optimization can be utilized to embed arbitrary trees in the hypercube and the q-dimensional mesh by using a similar algorithm of the randomized flip-bit algorithm, described by F.T. Leighton (1992). We show that these embedding algorithms embed any M-node tree in N-PEs hypercube or N-PE's q-dimensional mesh with load O(M/N), which is optimal for all M.