2022/05/26 by Hussam Al Daas, Daas, Hussam Al, Grey Ballard +7 · 1 citation
Computer Science · #Coding theory and cryptography #Distributed #FOS: Computer and information sciences #Interconnection Networks and Systems #Parallel #Quantum Computing Algorithms and Architecture #and Cluster Computing (cs.DC)
paper · pdf · doi:10.48550/arxiv.2205.13407
openalex publication_date 2022/05/26 · openalex created_date 2022/06/13 · openalex updated_date 2026/07/28
Communication lower bounds have long been established for matrix multiplication algorithms. However, most methods of asymptotic analysis have either ignored the constant factors or not obtained the tightest possible values. Recent work has demonstrated that more careful analysis improves the best known constants for some classical matrix multiplication lower bounds and helps to identify more efficient algorithms that match the leading-order terms in the lower bounds exactly and improve practical performance. The main result of this work is the establishment of memory-independent communication lower bounds with tight constants for parallel matrix multiplication. Our constants improve on previous work in each of three cases that depend on the relative sizes of the aspect ratios of the matrices.