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SIAM J. Comput. 39, pp. 979-1005 (27 pages)
Faster Integer Multiplication
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Add to FacebookFor more than 35 years, the fastest known method for integer multiplication has been the Schönhage–Strassen algorithm running in time $O(n\log n\log\log n)$. Under certain restrictive conditions, there is a corresponding $\Omega(n\log n)$ lower bound. All this time, the prevailing conjecture has been that the complexity of an optimal integer multiplication algorithm is $\Theta(n\log n)$. We take a major step towards closing the gap between the upper bound and the conjectured lower bound by presenting an algorithm running in time $n\log n\,2^{O(\log^*n)}$. The running time bound holds for multitape Turing machines. The same bound is valid for the size of Boolean circuits.
© 2009 Society for Industrial and Applied Mathematics
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Received December 27, 2007
Accepted June 16, 2009
Published online September 02, 2009
Accepted June 16, 2009
Published online September 02, 2009
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