Graph expansion analysis for communication costs of fast rectangular matrix multiplication

  • Authors:

  • Grey Ballard;James Demmel;Olga Holtz;Benjamin Lipshitz;Oded Schwartz

  • Affiliations:

  • EECS Department, University of California, Berkeley, CA;Mathematics Department and CS Division, University of California, Berkeley, CA;Departments of Mathematics, University of California, Berkeley, and Technische Universität, Berlin, Germany;EECS Department, University of California, Berkeley, CA;EECS Department, University of California, Berkeley, CA

  • Venue:
  • MedAlg'12 Proceedings of the First Mediterranean conference on Design and Analysis of Algorithms
  • Year:
  • 2012

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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.