Leslie G. Valiant
ABSTRACT
The purpose of this paper is to explore the possibility that purely graph-theoretic reasons may account for the superlinear complexity of wide classes of computational problems. The results are therefore of two kinds: reductions to graph theoretic conjectures on the one hand, and graph theoretic results on the other.
We show that the graph of any algorithm for any one of a number of arithmetic problems (e.g. polynomial multiplication, discrete Fourier transforms, matrix multiplication) must have properties closely related to concentration networks.
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Index Terms
- On non-linear lower bounds in computational complexity
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