Towards automatic parallelization of tree reductions in dynamic programming

Tree contraction algorithms, whose idea was first proposed by Miller and Reif, are important parallel algorithms to implement efficient parallel programs manipulating trees. Despite their efficiency, the tree contraction algorithms have not been widely used due to the difficulties in deriving the tree contracting operations. In particular, the derivation of the tree contracting operations is much difficult when multiple values are referred and updated in each step of the contractions. Such computations often appear in dynamic programming problems on trees. In this paper, we propose an algebraic approach to deriving tree contraction programs from recursive tree programs, by focusing on the properties of commutative semirings. We formalize a new condition for implementing tree reductions with the tree contraction algorithms, and give a systematic derivation of the tree contracting operations. Based on it, we implemented a code generator for tree reductions, which has an optimization me...

• Type: Conference
• Year: 2006
• Where: SPAA
• Authors: Kiminori Matsuzaki, Zhenjiang Hu, Masato Takeichi
• Keywords: Distributed And Parallel Computing, SPAA 2006, Tree, Tree Contracting Operations, Tree Contraction Algorithms