2009/02/13 by Richard Strong Bowen, Bowen, Richard Strong, Bo Chen +5
Computer Science · #Complexity and Algorithms in Graphs #Computational Complexity (cs.CC) #FOS: Computer and information sciences #Interconnection Networks and Systems #Matrix Theory and Algorithms #Symbolic Computation (cs.SC) #cs.CC #cs.SC
paper · pdf · doi:10.48550/arxiv.0902.2407
14 pages, 3 figures
arxiv created 2009/02/13 · openalex publication_date 2009/02/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A generalization of recent group-theoretic matrix multiplication algorithms to an analogue of the theory of partial matrix multiplication is presented. We demonstrate that the added flexibility of this approach can in some cases improve upper bounds on the exponent of matrix multiplication yielded by group-theoretic full matrix multiplication. The group theory behind our partial matrix multiplication algorithms leads to the problem of maximizing a quantity representing the "fullness" of a given partial matrix pattern. This problem is shown to be NP-hard, and two algorithms, one optimal and another non-optimal but polynomial-time, are given for solving it.