Graph Expansion Analysis for Communication Costs of Fast Rectangular Matrix Multiplication

  • Grey Ballard
  • James Demmel
  • Olga Holtz
  • Benjamin Lipshitz
  • Oded Schwartz
Conference paper

DOI: 10.1007/978-3-642-34862-4_2

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7659)
Cite this paper as:
Ballard G., Demmel J., Holtz O., Lipshitz B., Schwartz O. (2012) Graph Expansion Analysis for Communication Costs of Fast Rectangular Matrix Multiplication. In: Even G., Rawitz D. (eds) Design and Analysis of Algorithms. Lecture Notes in Computer Science, vol 7659. Springer, Berlin, Heidelberg

Abstract

Graph expansion analysis of computational DAGs is useful for obtaining communication cost lower bounds where previous methods, such as geometric embedding, are not applicable. This has recently been demonstrated for Strassen’s and Strassen-like fast square matrix multiplication algorithms. Here we extend the expansion analysis approach to fast algorithms for rectangular matrix multiplication, obtaining a new class of communication cost lower bounds. These apply, for example to the algorithms of Bini et al. (1979) and the algorithms of Hopcroft and Kerr (1971). Some of our bounds are proved to be optimal.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Grey Ballard
    • 1
  • James Demmel
    • 2
  • Olga Holtz
    • 3
    • 4
  • Benjamin Lipshitz
    • 1
  • Oded Schwartz
    • 1
  1. 1.EECS DepartmentUniversity of CaliforniaBerkeleyUS
  2. 2.Mathematics Department and CS DivisionUniversity of CaliforniaBerkeleyUSA
  3. 3.Departments of MathematicsUniversity of CaliforniaBerkeleyUSA
  4. 4.Technische UniversitätBerlinGermany

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