Name
Abstract | ||
|---|---|---|
We further develop the group-theoretic approach to fast matrix multiplication introduced by Cohn and Umans, and for the first time use it to derive algorithms asymptotically faster than the standard algorithm. We describe several families of wreath product groups that achieve matrix multiplication exponent less than 3, the asymptotically fastest of which achieves exponent 2.41. We present two conjectures regarding specific improvements, one combinatorial and the other algebraic. Either one would imply that the exponent of matrix multiplication is 2. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1109/SFCS.2005.39 | 46TH ANNUAL IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE, PROCEEDINGS |
Keywords | Field | DocType |
group theory,wreath product,matrix multiplication | Scalar multiplication,Matrix chain multiplication,Multiplication,Discrete mathematics,Combinatorics,Multiplication algorithm,Algebra,Algorithm,Strassen algorithm,Diagonal matrix,Matrix multiplication,Mathematics,Block matrix | Conference |
ISSN | Citations | PageRank |
0272-5428 | 30 | 2.95 |
References | Authors | |
3 | 4 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Henry Cohn | 1 | 192 | 20.23 |
| Robert Kleinberg | 2 | 2886 | 202.55 |
| Balázs Szegedy | 3 | 285 | 26.04 |
| Christopher Umans | 4 | 879 | 55.36 |