Parallel Blocked Algorithm for Solving the Algebraic Path Problem on a Matrix Processor

Takahashi, Akihito; Sedukhin, Stanislav G.

doi:10.1007/11557654_89

Cited by 8 publications

(8 citation statements)

References 9 publications

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“…[2], [19], [20]. Thus, the developed APSP program can be used for the solution of these problems with small modifications to satisfy different algebras.…”

Section: Discussionmentioning

confidence: 99%

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A Solution of the All-Pairs Shortest Paths Problem on the Cell Broadband Engine Processor

Matsumoto

Sedukhin

2009

IEICE Trans. Inf. & Syst.

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SUMMARYThe All-Pairs Shortest Paths (APSP) problem is a graph problem which can be solved by a three-nested loop program. The Cell Broadband Engine (Cell/B.E.) is a heterogeneous multi-core processor that offers the high single precision floating-point performance. In this paper, a solution of the APSP problem on the Cell/B.E. is presented. To maximize the performance of the Cell/B.E., a blocked algorithm for the APSP problem is used. The blocked algorithm enables reuse of data in registers and utilizes the memory hierarchy. We also describe several optimization techniques for effective implementation of the APSP problem on the Cell/B.E.

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“…[2], [19], [20]. Thus, the developed APSP program can be used for the solution of these problems with small modifications to satisfy different algebras.…”

Section: Discussionmentioning

confidence: 99%

“…in Sony PlayStation3. The implemented blocked algorithm for the APSP problem is similar to the algorithms in [5], [20]. The most computational intensive part of the blocked algorithm is calculated by matrix multiplication in a corresponding algebraic semiring.…”

Section: Introductionmentioning

confidence: 99%

A Solution of the All-Pairs Shortest Paths Problem on the Cell Broadband Engine Processor

Matsumoto

Sedukhin

2009

IEICE Trans. Inf. & Syst.

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“…The algorithm for solving algebraic path problem boils down to find the Kleene closure of adjacency matrix, i.e., the summation of all non-negative integer powers of the adjacency matrix [4]. Since then, with an in-depth study, Gauβ-Jordan elimination method has been improved from every angle and its application has a gradual expansion from some special semirings first to general cases, and the computing power with the introduction of advanced technologies such as parallel computing has been greatly improved [5][6][7][8][9][10][11][12]. However, the semirings applied to Gauβ-Jordan elimination method always required completeness and closeness.…”

Section: Introductionmentioning

confidence: 99%

An Algorithm of Plus-Closures of Loop-Nonnegative Matrices over Idempotent Semirings and its Applications

Wang¹,

Hu²,

Liu³

2013

Proceedings of the 2nd International Conference on Computer Science and Electronics Engineering (ICCSEE 2013)

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Abstract-To judge the loop-nonnegativity of a matrix A over an idempotent semiring and compute the plus-closure of A when it is loop-nonnegative, a Plus_Closure_of_Matrix algorithm of complexity 3 ( ) O n is constructed and proved. As a generalization of Floyd algorithm, Warshall algorithm as well as Gauβ-Jordan Elimination algorithm on idempotent semirings, this algorithm can also be used to solve some Algebraic Path Problems, Shortest Path Problems and the transitive closures of matrices over idempotent semirings even if the idempotent semirings have no completeness and closeness.

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“…The algorithm for solving algebraic path problem boiled down to find the Kleene closure of adjacency matrix, i.e., the summation of all nonnegative integer powers of the adjacency matrix [6]. Since then, with an in-depth study, Gauβ-Jordan elimination method has been improved from every angle and its application has a gradual expansion from some special semirings first to general cases, and the computing power with the introduction of advanced technologies such as parallel computing has been greatly improved [7][8][9][10][11][12][13][14]. However, the semirings applied to Gauβ-Jordan elimination method always required completeness and closeness.…”

Section: Introductionmentioning

confidence: 99%

The Transitive-Closures of Matrices over Idempotent Semirings and its Applications

Wang¹,

He²,

Hu³

2013

Proceedings of the 2013 International Conference on Advanced Computer Science and Electronics Information

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-The Algebraic Path Problem is an important issue with a broad background. Consider the problem to solve the algebraic path problem can be concluded to find the Kleene closure of the adjacency matrix, an algorithm of time complexity 3 ( ) O n to find the transitive closure of matrices over idempotent semiring is constructed, as well as the conditions applicable to it are provided. Compared with the Gauβ-Jordan elimination, this algorithm could extend the applicable range to certain semirings which do not have completeness and closeness, Thus, it has a wide application since it can provide a new method to solve the algebraic path problem over idempotent semirings which do not have completeness and closeness.

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Parallel Blocked Algorithm for Solving the Algebraic Path Problem on a Matrix Processor

Cited by 8 publications

References 9 publications

A Solution of the All-Pairs Shortest Paths Problem on the Cell Broadband Engine Processor

A Solution of the All-Pairs Shortest Paths Problem on the Cell Broadband Engine Processor

An Algorithm of Plus-Closures of Loop-Nonnegative Matrices over Idempotent Semirings and its Applications

The Transitive-Closures of Matrices over Idempotent Semirings and its Applications

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