Uniquely Solvable Puzzles and Fast Matrix Multiplication
نویسندگان
چکیده
In 2003 Cohn and Umans introduced a new group-theoretic framework for doing fast matrix multiplications, with several conjectures that would imply the matrix multiplication exponent ω is 2. Their methods have been used to match one of the fastest known algorithms by Coppersmith and Winograd, which runs in O(n2.376) time and implies that ω ≤ 2.376. This thesis discusses the framework that Cohn and Umans came up with and presents some new results in constructing uniquely solvable puzzles that were introduced in a 2005 follow-up paper, and which play a crucial role in one of the ω = 2 conjectures.
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