(0, 1)-Matrix-Vector Products via Compression by Induction of Hierarchical Grammars
نویسندگان
چکیده
We demonstrate a method for reducing the number of arithmetic operations within a (0, 1)matrix vector product. We employ an algorithm, SEQUITUR, developed for lossless text compression, which generates a context free grammar derived from an inherent hierarchy of repeated sequences. In this context, the sequences are composed of bit patterns for a set of adjacent columns. This grammar will represent the original matrix as a hierarchical set of rules identifying and exploiting structural redundancies. It is then sufficient to compute the inner product value of that pattern only once. When that pattern reappears in a different row, that inner product value is reloaded rather than recomputed, thus obviating computations for each repetition.
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