A Practical Tree Contraction Algorithm for Parallel Skeletons on Trees of Unbounded Degree

Algorithmic skeletons are ready-made parallel computation patterns. Since each skeleton can be evaluated efficiently on parallel computation environments, we can develop effcient parallel programs only by specifying our computation by a combination of skeletons. Although effectiveness of algorithmic skeletons, especially those manipulating arrays and lists, is now well-recognized, those for trees of unbounded degree have not been firmly established. Most of the existing studies transform them to binary trees through preprocessing. But this approach is not practical. The transformation not only makes developments of parallel programs diffcult but also affects the performance of the parallel programs developed.In this paper, we propose a parallel tree contraction algorithm named Rake-Shunt contraction algorithm. It is generalization of the Shunt contraction algorithm, which has been used as the algorithmic basis of the binary-tree skeletons, and inherits several good properties such as scalability with respect to the number of processors and simplicity of the implementation. Moreover, it can deal with arbitrary trees and requires no modification of their shapes. Our preliminary experiments show that our algorithm leads to an implementation of the tree reduction, one of the most important tree skeletons, that is easier to use and more effcient than the previous method based on the transformation to binary trees.