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The Coppersmith–Winograd algorithm is frequently used as a building block in other algorithms to prove theoretical time bounds.
However, unlike the Strassen algorithm, it is not used in practice because it only provides an advantage for matrices so large that they cannot be processed by modern hardware.<ref>{{Citation | last1=Robinson | first1=Sara | title=Toward an Optimal Algorithm for Matrix Multiplication | url=
[[Henry Cohn]], [[Robert Kleinberg]], [[Balázs Szegedy]] and [[Chris Umans]] have re-derived the Coppersmith–Winograd algorithm using a [[group theory|group-theoretic]] construction. They also showed that either of two different conjectures would imply that the optimal exponent of matrix multiplication is 2, as has long been suspected. However, they were not able to formulate a specific solution leading to a better running-time than Coppersmith–Winograd.<ref>{{Cite book | last1 = Cohn | first1 = H. | last2 = Kleinberg | first2 = R. | last3 = Szegedy | first3 = B. | last4 = Umans | first4 = C. | chapter = Group-theoretic Algorithms for Matrix Multiplication | doi = 10.1109/SFCS.2005.39 | title = 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05) | pages = 379 | year = 2005 | isbn = 0-7695-2468-0 | pmid = | pmc = }}</ref> Several of their conjectures have since been disproven by Blasiak, Cohn, Church, Grochow, Naslund, Sawin, and Umans using the Slice Rank method.<ref>{{Cite book | last1 = Blasiak | first1 = J. | last2 = Cohn | first2 = H. | last3 = Church | first3 = T. | last4 = Grochow | first4 = J. | last5 = Naslund | first5= E. | last6 = Sawin | first6 = W. | last7=Umans | first7= C.| chapter= On cap sets and the group-theoretic approach to matrix multiplication | doi = 10.19086/da.1245 | title = Discrete Analysis | url = http://discreteanalysisjournal.com/article/1245-on-cap-sets-and-the-group-theoretic-approach-to-matrix-multiplication}}</ref>
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