Matrix decomposition on the star graph

Abdel Elah Al-Ayyoub, Khaled Day

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

We present and evaluate, for the first time, a parallel algorithm for solving the LU decomposition problem on the star graph. The proposed parallel algorithm is of O(N 3/n!) computation complexity and uses O(Nn) communication time to decompose a matrix of order N on a star graph of dimension n, where N≥(n - 1)!. The incurred communication time is better than the best known results for the hypercube, O(N log n!), and the mesh, O(N√n!), each with approximately n! nodes. The proposed parallel algorithm takes advantage of the attractive topological qualities of the star graph in order to reduce the communication time involved in tasks such as pivoting, row/column interchanges, and pivot row and multipliers column broadcasts.

Original languageEnglish
Pages (from-to)803-812
Number of pages10
JournalIEEE Transactions on Parallel and Distributed Systems
Volume8
Issue number8
DOIs
Publication statusPublished - 1997

Fingerprint

Star Graph
Matrix Decomposition
Parallel algorithms
Parallel Algorithms
Stars
Decomposition
Decompose a matrix
Communication
LU decomposition
Pivoting
Pivot
Interchanges
Hypercube
Broadcast
Multiplier
Mesh
Evaluate
Vertex of a graph

Keywords

  • Interconnection networks
  • Matrix decomposition
  • Parallel processing
  • Star graphs

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Theoretical Computer Science
  • Computational Theory and Mathematics

Cite this

Matrix decomposition on the star graph. / Al-Ayyoub, Abdel Elah; Day, Khaled.

In: IEEE Transactions on Parallel and Distributed Systems, Vol. 8, No. 8, 1997, p. 803-812.

Research output: Contribution to journalArticle

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