Parallel Programming with Tree Skeletons

Parallel computing is an essential technique to deal with large scaled problems. In recent years, while hardware for parallel computing is getting widely available, developing software for parallel computing remains as a hard task for many programmers. The main difficulties are caused by the communication, synchronization, and data distribution required in parallel programs. This thesis studies the theory and practice of parallel programming for trees based on parallel primitives called tree skeletons. Trees are important data structures for representing structured data. However, their irregular and ill-balanced structure makes it hard to develop efficient parallel programs on them, because naive divide-and-conquer parallel computation may lead to poor performance for ill-balanced trees. To remedy this situation, this thesis develops a new framework for parallel programming for trees on the basis of the programming model called skeletal parallel programming. Skeletal parallel programming, first proposed by Cole, encourages programmers to develop parallel programs by composing ready-made components called parallel skeletons (or algorithmic skeletons). A theory has been proposed for design of parallel skeletons for lists based on constructive algorithms, and several libraries of parallel skeletons have been developed to bring the theory into practice. This thesis extends these ideas from lists to trees. The following are three important contributions in the thesis. The first contribution is the design of parallel tree skeletons for both binary trees and general trees of arbitrary shape. Our parallel tree skeletons have a sequential interface but with a parallel implementation; the sequential interface is designed based on the theory of constructive algorithmics, while the parallel implementation is either based on tree contraction algorithms or newly developed ones. The second contribution is a set of theories for skeletal parallel programming on trees. These theories provide us with a systematic method for deriving skeletal parallel programs from sequential programs. We illustrate effectiveness of the method by solving two classes of nontrivial problems, maximum marking problems and XPath queries. The third contribution is an implementation of a parallel skeleton library for trees. We developed a new implementation algorithm for tree skeletons, in which a tree is divided with high locality and good load balance and tree skeletons are executed efficiently in