  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.
