The work reported in this talk represents a step toward that goal. We show how certain problems can be formulated in the framework of "generalized multilinear algebra." We can then use group- theoretical tools to express the computation in an architecture- neutral manner so that it can be implemented efficiently on many high-performance computers.
Our paradigm was applied to various domains included AI (planning and search), computational chemistry, N-body code, and signal processing. The fastest available implementations for problems from several of these domains were obtained.
After introducing our paradigm and surveying our empirical results, this talk will focus on what I think are two of the most interesting case studies: chess endgames and group Fourier transforms. Our chess endgame program discovered a forced 223-move win in a position that had been thought drawn and our group Fourier transform program resulted in the fastest implementations of certain non-abelian group Fourier transforms, which are a beautiful and exciting generalization of classical Fourier transforms with applications to data analysis, learning, compression, and vision. If time permits I will also describe new parallel algorithms for knapsack and AI planning.
HOST: Prof. S. Ward
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Modified: Jun 25, 1997|
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