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A new general parallel algorithmic technique,for computations,on trees is presented. The new technique performs a reduction of the tree expression evaluation problem,to list ranking; then, the list ranking provides a schedule for evaluating the tree operations. The technique needs logarithmic time usingan,optimal number,of processors and has applications to other tree problems. This new technique enables us to systematically order four basic ideas and,techniques for parallel algorithms on tree: (1) The list ranking problem. (2) The Euler tour technique on trees. (3) The centroid decomposition technique. (4) The new,accelerated centroid decomposition,(ACD)technique.

The accelerated centroid decomposition technique for optimal parallel tree evaluation in logarithmic time