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Communication lower bounds have long been established for matrixmultiplication algorithms. However, most methods of asymptotic analysis haveeither ignored the constant factors or not obtained the tightest possiblevalues. Recent work has demonstrated that more careful analysis improves thebest known constants for some classical matrix multiplication lower bounds andhelps to identify more efficient algorithms that match the leading-order termsin the lower bounds exactly and improve practical performance. The main resultof this work is the establishment of memory-independent communication lowerbounds with tight constants for parallel matrix multiplication. Our constantsimprove on previous work in each of three cases that depend on the relativesizes of the aspect ratios of the matrices.

Tight Memory-Independent Parallel Matrix Multiplication Communication Lower Bounds