Strategy-Accurate Parallel Buchberger Algorithms

Attardi, Giuseppe; Traverso, Carlo Enrico

doi:10.1006/jsco.1996.0022

Cited by 21 publications

(15 citation statements)

References 15 publications

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“…In the Gröbner basis case, Faugère's (1994) parallelization is strategy compliant, but it is based on modular computations that have no analogue in term completion. Attardi and Traverso (1994) have designed a strategy compliant parallel Gröbner basis algorithm similar to ours, but so far the empirical results are limited † .…”

Section: Motivationmentioning

confidence: 98%

Strategy Compliant Multi-Threaded Term Completion

Bündgen

Göbel

Küchlin

1996

Journal of Symbolic Computation

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We report on the design, implementation, and performance, of the parallel term-rewriting system PaReDuX. We discuss the parallelization of three term completion procedures: Knuth-Bendix completion, completion modulo AC, and unfailing completion. Our parallelization is strategy-compliant, i.e., the parallel code performs exactly the same work as the sequential code, but the work load is shared by many processors. PaReDuX is designed for shared memory parallel architectures, such as multi-processor workstations, where it shows good performance on a variety of examples.

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Section: Motivationmentioning

confidence: 98%

Strategy Compliant Multi-Threaded Term Completion

Bündgen

Göbel

Küchlin

1996

Journal of Symbolic Computation

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“…The first two equations together with the second defining equation of X (1) give NPD contains exhaustive information about the ideal I and, in particular, the scheme Spec(R/I) due to the possibility of solving the ideal membership problem. This is so, since for every Y the projection π d Y (z) of a witness point z ∈ wY gives a generic point of Y and in the view of the following:…”

Section: Generalized and Classical Witness Setsmentioning

confidence: 99%

“…(Although there is no doubt that limited speedups are possible in parallel Gröbner computation, the claims of good scalability are substantiated with experiments on preselected classes of problems and methods based on non-optimal serial algorithms. See, e.g., [1] for critique of such claims. ) We live in the age when the clock speed of processors has stopped growing fast and the computational capacity of computers increases mainly through building either multicore or distributed systems.…”

Section: Introductionmentioning

confidence: 96%

Numerical primary decomposition

Leykin¹

2008

Proceedings of the Twenty-First International Symposium on Symbolic and Algebraic Computation

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Consider an ideal I ⊂ R = C[x1, . . . , xn] defining a complex affine variety X ⊂ C n . We describe the components associated to I by means of numerical primary decomposition (NPD).The method is based on the construction of deflation ideal I (d) that defines the deflated variety X (d) in a complex space of higher dimension. For every embedded component there exists d and an isolated component Y (d) of I (d) projecting onto Y . In turn, Y (d) can be discovered by existing methods for prime decomposition, in particular, the numerical irreducible decomposition, applied to X (d) .The concept of NPD gives a full description of the scheme Spec(R/I) by representing each component with a witness set. We propose an algorithm to produce a collection of witness sets that contains a NPD and that can be used to solve the ideal membership problem for I.

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“…Annotating this loop by spec(P airs) mark we open the possibilities to initiate speculative parallel computing of certain iterations. If for some element of P airs speculative computing is initiated and after this moment according to B-criterion [1] for current completing of P airs this element is eleminated, then speculative process initiated by it will also be killed by corresponding mechanism of SDP.…”

Section: Buchberger's Algorithmmentioning

confidence: 99%

Parallelizing of Sequential Programs on the Basis of Pipeline and Speculative Features of the Operators*

Godlevsky

Gazák

Hluchý

1999

Lecture Notes in Computer Science

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Abstract. An approach to dynamic parallelizing of coarse grained program where the parallelization sources are both dataflow analysis and the features pointed out in the program by annotating is proposed. Program annotating enables to hold two additional types of parallel computations which cannot be found out only from the analysis of dataflow dependences. Firstly, there are speculative computations based on anticipating alternative branches of the program's computational process. Secondly, there are pipeline computations that sometimes may be initialised for operators at the moment when their input data are not complete. Automated program analysis of this type of concurrence is either very hard or it generates a lot of surplus computation, thus absorbing the effect of program parallelization. The implementation of the system of dynamic program parallelization for clusters of PCs and results of some experiments performed on it are described.

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Strategy-Accurate Parallel Buchberger Algorithms

Cited by 21 publications

References 15 publications

Strategy Compliant Multi-Threaded Term Completion

Strategy Compliant Multi-Threaded Term Completion

Numerical primary decomposition

Parallelizing of Sequential Programs on the Basis of Pipeline and Speculative Features of the Operators*

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