Software, Environments, and Tools
Graph Algorithms in the Language of Linear Algebra

5. Fundamental Graph Algorithms

Abstract

This chapter discusses the representation of several fundamental graph algorithms as algebraic operations. Even though the underlying algorithms already exist, the algebraic representation allows for easily expressible efficient algorithms with appropriate matrix constructs. This chapter gives algorithms for single-source shortest paths, all-pairs shortest paths, and minimum spanning tree.

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Published In

cover image Software, Environments, and Tools
Graph Algorithms in the Language of Linear Algebra
Pages: 45 - 58
Editors: Jeremy Kepner and John Gilbert
ISBN (Print): 978-0-89871-990-1
ISBN (Online): 978-0-89871-991-8

History

Published online: 23 March 2012

Keywords

  1. graph algorithms
  2. network analysis
  3. adjacency matrix
  4. sparse matrices
  5. parallel programming
  6. combinatorial scientific computing

Keywords

  1. 48
  2. 05
  3. 01
  4. 07
  5. 08

Keywords

  1. 511'.6--dc22

Keywords

    QA166.245.K47 2011Graph algorithms, Algebras, Linear

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