Group-Theoretic Partial Matrix Multiplication

Details Group-Theoretic Partial Matrix Multiplication Group-Theoretic Partial Matrix Multiplication

2009-02-13

arxiv.org/abs/0902.2407v1

Computer Science

Computational Complexity

14 pages, 3 figures

Scientific paper

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.

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