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Graph expansion analysis of computational DAGs is useful for obtainingcommunication cost lower bounds where previous methods, such as geometricembedding, are not applicable. This has recently been demonstrated forStrassen's and Strassen-like fast square matrix multiplication algorithms. Herewe extend the expansion analysis approach to fast algorithms for rectangularmatrix multiplication, obtaining a new class of communication cost lowerbounds. These apply, for example to the algorithms of Bini et al. (1979) andthe algorithms of Hopcroft and Kerr (1971). Some of our bounds are proved to beoptimal.

Graph Expansion Analysis for Communication Costs of Fast Rectangular Matrix Multiplication