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Automatic Inversion Generates DivideandConquer Parallel Programs
"... Divideandconquer algorithms are suitable for modern parallel machines, tending to have large amounts of inherent parallelism and working well with caches and deep memory hierarchies. Among others, list homomorphisms are a class of recursive functions on lists, which match very well with the divide ..."
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Divideandconquer algorithms are suitable for modern parallel machines, tending to have large amounts of inherent parallelism and working well with caches and deep memory hierarchies. Among others, list homomorphisms are a class of recursive functions on lists, which match very well with the divideandconquer paradigm. However, direct programming with list homomorphisms is a challenge for many programmers. In this paper, we propose and implement a novel system that can automatically derive costoptimal list homomorphisms from a pair of sequential programs, based on the third homomorphism theorem. Our idea is to reduce extraction of list homomorphisms to derivation of weak right inverses. We show that a weak right inverse always exists and can be automatically generated from a wide class of sequential programs. We demonstrate our system with several nontrivial examples, including the maximum prefix sum problem, the prefix sum computation, the maximum segment sum problem, and the lineofsight problem. The experimental results show practical efficiency of our automatic parallelization algorithm and good speedups of the generated parallel programs.
Systematic Derivation of Tree Contraction Algorithms
 In Proceedings of INFOCOM '90
, 2005
"... While tree contraction algorithms play an important role in e#cient tree computation in parallel, it is di#cult to develop such algorithms due to the strict conditions imposed on contracting operators. In this paper, we propose a systematic method of deriving e#cient tree contraction algorithms f ..."
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While tree contraction algorithms play an important role in e#cient tree computation in parallel, it is di#cult to develop such algorithms due to the strict conditions imposed on contracting operators. In this paper, we propose a systematic method of deriving e#cient tree contraction algorithms from recursive functions on trees in any shape. We identify a general recursive form that can be parallelized to obtain e#cient tree contraction algorithms, and present a derivation strategy for transforming general recursive functions to parallelizable form. We illustrate our approach by deriving a novel parallel algorithm for the maximum connectedset sum problem on arbitrary trees, the treeversion of the famous maximum segment sum problem.
Design and implementation of general tree skeletons
, 2005
"... The METR technical reports are published as a means to ensure timely dissemination of scholarly and technical work on a noncommercial basis. Copyright and all rights therein are maintained by the authors or by other copyright holders, notwithstanding that they have offered their works here electron ..."
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Cited by 1 (1 self)
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The METR technical reports are published as a means to ensure timely dissemination of scholarly and technical work on a noncommercial basis. Copyright and all rights therein are maintained by the authors or by other copyright holders, notwithstanding that they have offered their works here electronically. It is understood that all persons copying this information will adhere to the terms and constraints invoked by each author’s copyright. These works may not be reposted without the explicit permission of the copyright holder.
Experimentation, Theory
"... 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 tr ..."
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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 mechanism that can remove unnecessary computations in the derived parallel programs. As far as we are aware, this is the first step towards an automatic parallelization system for the development of efficient tree programs.
Abstract Parallel skeletons for manipulating general trees
, 2006
"... Trees are important datatypes that are often used in representing structured data such as XML. Though trees are widely used in sequential programming, it is hard to write efficient parallel programs manipulating trees, because of their irregular and illbalanced structures. In this paper, we propose ..."
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Trees are important datatypes that are often used in representing structured data such as XML. Though trees are widely used in sequential programming, it is hard to write efficient parallel programs manipulating trees, because of their irregular and illbalanced structures. In this paper, we propose a solution based on the skeletal approach. We formalize a set of skeletons (abstracted computational patterns) for rose trees (general trees of arbitrary shapes) based on the theory of Constructive Algorithmics. Our skeletons for rose trees are extensions of those proposed for lists and binary trees. We show that we can implement the skeletons efficiently in parallel, by combining the parallel binarytree skeletons for which efficient parallel implementations are already known. As far as we are aware, we are the first who have formalized and implemented a set of simple but expressive parallel skeletons for rose trees. Ó 2006 Elsevier B.V. All rights reserved.
Parallel Processing Letters, ❢c World Scientific Publishing Company SYSTEMATIC DERIVATION OF TREE CONTRACTION ALGORITHMS ∗
, 2004
"... While tree contraction algorithms play an important role in efficient tree computation in parallel, it is difficult to develop such algorithms due to the strict conditions imposed on contracting operators. In this paper, we propose a systematic method of deriving efficient tree contraction algorithm ..."
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While tree contraction algorithms play an important role in efficient tree computation in parallel, it is difficult to develop such algorithms due to the strict conditions imposed on contracting operators. In this paper, we propose a systematic method of deriving efficient tree contraction algorithms from recursive functions on trees. We identify a general recursive form that can be parallelized into efficient tree contraction algorithms, and present a derivation strategy for transforming general recursive functions to the parallelizable form. We illustrate our approach by deriving a novel parallel algorithm for the maximum connectedset sum problem on arbitrary trees, the treeversion of the wellknown maximum segment sum problem.
Automatic Interprocedural Parallelization
"... In this paper, we introduce a novel technique for automatic parallelization of independent procedures. Our proposed technique identifies the potentially independent procedure calls and generates code for executing them in parallel without the intervention of the programmer. Our major concern is to p ..."
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In this paper, we introduce a novel technique for automatic parallelization of independent procedures. Our proposed technique identifies the potentially independent procedure calls and generates code for executing them in parallel without the intervention of the programmer. Our major concern is to parallelize those function calls that consume a significant portion of the execution time like recursive function calls and functions calls inside a loop. The proposed technique uses a hybrid approach, which involves both static and dynamic (or runtime) analysis. To reduce the overhead of speculative runtime analysis we extend a technique called Sensitivity Analysis (originally developed for loops) to recursive procedures. If a procedure call is identified as a candidate for parallel execution then OpenMP constructs for executing the function call in parallel are generated. Generating OpenMP constructs has two major advantages, firstly it makes the program easy to understand and debug. Secondly it increases the portability of the program. I.