MATHEMATICAL ENGINEERING TECHNICAL REPORTS A Parallel Tree Contraction Algorithm on Non-Binary Trees

Parallel tree contraction is an important framework to develop efficient parallel algorithms on trees. Parallel tree contraction gives an appropriate scheduling for parallel computations on trees, and the scheduling brings efficient parallel algorithms to us. While there are many studies for efficient algorithms of parallel tree contraction and implementation of various parallel computations based on them, few studies give practical parallel tree contraction algorithms on non-binary trees. Some studies just mention that any tree can be encoded as a binary tree; however, binary-tree encoding breaks the original structure, and this makes it difficult to develop parallel algorithms following parallel tree contraction algorithms. In this paper, we propose a new parallel tree contraction algorithm. Our algorithm is a generalization of that proposed by Abrahamson et al., and works well even for nonbinary trees. Our algorithm requires no binary-tree encoding, and thus, it is easy to develop parallel algorithms based on our parallel tree contraction algorithm. In addition, we show sufficient conditions when computations can be parallelized based on our algorithm, and the conditions are generalizations of those known on binary trees.