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Generic Downwards Accumulations
 Science of Computer Programming
, 2000
"... . A downwards accumulation is a higherorder operation that distributes information downwards through a data structure, from the root towards the leaves. The concept was originally introduced in an ad hoc way for just a couple of kinds of tree. We generalize the concept to an arbitrary regular d ..."
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Cited by 25 (6 self)
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. A downwards accumulation is a higherorder operation that distributes information downwards through a data structure, from the root towards the leaves. The concept was originally introduced in an ad hoc way for just a couple of kinds of tree. We generalize the concept to an arbitrary regular datatype; the resulting denition is coinductive. 1 Introduction The notion of scans or accumulations on lists is well known, and has proved very fruitful for expressing and calculating with programs involving lists [4]. Gibbons [7, 8] generalizes the notion of accumulation to various kinds of tree; that generalization too has proved fruitful, underlying the derivations of a number of tree algorithms, such as the parallel prex algorithm for prex sums [15, 8], Reingold and Tilford's algorithm for drawing trees tidily [21, 9], and algorithms for query evaluation in structured text [16, 23]. There are two varieties of accumulation on lists: leftwards and rightwards. Leftwards accumulation ...
Parallel Implementation of Tree Skeletons
 Journal of Parallel and Distributed Computing
, 1996
"... Trees are a useful data type, but they are not routinely included in parallel programming systems because their irregular structure makes them seem hard to compute with e ciently. Wepresent a method for constructing implementations of skeletons, highlevel homomorphic operations on trees, that execu ..."
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Cited by 18 (2 self)
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Trees are a useful data type, but they are not routinely included in parallel programming systems because their irregular structure makes them seem hard to compute with e ciently. Wepresent a method for constructing implementations of skeletons, highlevel homomorphic operations on trees, that execute in parallel. In particular, we consider the case where the size of the tree is much larger than the the number of processors available, so that tree data must be partitioned. The approach uses the theory of categorical data types to derive implementation templates based on tree contraction. Many useful tree operations can be computed in time logarithmic in the size of their argument, on a wide range of parallel systems. 1 Contribution One common approach to generalpurpose parallel computation is based on packaging complex operations as templates, or skeletons [3, 12]. Skeletons encapsulate the control and data ow necessary to compute useful operations. This permits software to be written in a way that is independent of particular architectures, and indeed of underlying parallelism at all, while freeing implementations
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.
A generalisation of indexing for parallel document search
, 1995
"... Parallelism is useful in the storage and access of structured documents. Fast parallel algorithms for search in structured text are already known, but they will not supplant the use of indexes to speed up searching until massively parallel architectures become routinely available. However, parallel ..."
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Cited by 2 (1 self)
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Parallelism is useful in the storage and access of structured documents. Fast parallel algorithms for search in structured text are already known, but they will not supplant the use of indexes to speed up searching until massively parallel architectures become routinely available. However, parallel algorithms suggest new kinds of indexes that provide powerful search capability and performance even on modestlyparallel computers. We present a generalisation of indexes based on regular languages, called indexing languages, that are chosen to be homomorphic images of languages generated by typical search patterns. Precomputing properties of text strings relative to indexing languages makes it fast to exclude large parts of the text from consideration before executing a direct search. 1 1
Efficient Implementation of Tree Skeletons on DistributedMemory Parallel Computers
, 2006
"... 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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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.
A MapReduce Style Framework for Trees
"... Abstract—The emergence of cloud computing and Google’s MapReduce paradigm is renewing interest in the development of broadly applicable high level abstractions as a means to deliver easy programmability and cyber resources, while hiding complexities of system architecture, heterogeneity, faulttoler ..."
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Abstract—The emergence of cloud computing and Google’s MapReduce paradigm is renewing interest in the development of broadly applicable high level abstractions as a means to deliver easy programmability and cyber resources, while hiding complexities of system architecture, heterogeneity, faulttolerance, and parallel algorithms. In this paper, we present a highlevel framework for searches and computations on tree structures. Despite the diversity and types of tree structures, and the algorithmic ways in which they are utilized, our abstraction provides sufficient generality to be broadly applicable. We show how a number of basic tree operations can be cast in terms of our framework, and further demonstrate its applicability by solving two applications – knearest neighbors and manybody simulations – by merely using the proposed framework in multiple ways. Finally, we discuss algorithmic strategies for building such a framework to enable treebased applications on parallel systems. I.
An Effective Data Placement Strategy for XML Documents
"... Abstract. As XML is increasingly being used in Web applications, new technologies need to be investigated for processing XML documents with high performance. Parallelism is a promising solution for structured document processing and data placement is a major factor for system performance improvement ..."
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Abstract. As XML is increasingly being used in Web applications, new technologies need to be investigated for processing XML documents with high performance. Parallelism is a promising solution for structured document processing and data placement is a major factor for system performance improvement in parallel processing. This paper describes an effective XML document data placement strategy. The new strategy is based on a multilevel graph partitioning algorithm with the consideration of the unique features of XML documents and query distributions. A new algorithm, which is based on XML query schemas to derive the weighted graph from the labelled directed graph presentation of XML documents, is also proposed. Performance analysis on the algorithm presented in the paper shows that the new data placement strategy exhibits low workload skew and a high degree of parallelism.
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.