Graduation Year
2012
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
Reader 1
Michael Orrison
Reader 2
Nicholas Pippenger
Terms of Use & License Information
Rights Information
© Palmer Mebane
Abstract
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 $\omega$ is 2. Their methods have been used to match one of the fastest known algorithms by Coppersmith and Winograd, which runs in $O(n^{2.376})$ time and implies that $\omega \leq 2.376$. This thesis discusses the framework that Cohn and Umans came up with and presents some new results in constructing combinatorial objects called uniquely solvable puzzles that were introduced in a 2005 follow-up paper, and which play a crucial role in one of the $\omega = 2$ conjectures.
Recommended Citation
Mebane, Palmer, "Uniquely Solvable Puzzles and Fast Matrix Multiplication" (2012). HMC Senior Theses. 37.
https://scholarship.claremont.edu/hmc_theses/37
