Parallelization with tree skeletons

Abstract. Trees are useful data structures, but to design efficient parallel programs over trees is known to be more difficult than to do over lists. Although several important tree skeletons have been proposed to simplify parallel programming on trees, few studies have been reported on how to systematically use them in solving practical problems; it is neither clear how to make a good combination of skeletons to solve a given problem, nor obvious even how to find suitable operators used in a single skeleton. In this paper, we report our first attempt to resolve these problems, proposing two important transformations, the tree diffusion transformation and the tree context preservation transformation. The tree diffusion transformation allows one to use familiar recursive definitions to develop his parallel programs, while the tree context preservation transformation shows how to derive associative operators that are required when using tree skeletons. We illustrate our approach by deriving an efficient parallel program for solving a nontrivial problem called the party planning problem, the tree version of the famous maximum-weight-sum problem