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SIAM J. on Computing / Volume 39 / Issue 3

SIAM J. Comput. 39, pp. 979-1005 (27 pages)

Faster Integer Multiplication

Martin Fürer

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For 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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KEYWORDS

AMS Subject Headings

68W30, 68W40, 68Q25

PUBLICATION DATA

ISSN:

0097-5397 (print)  
1095-7111 (online)

Publisher:

$abstract.society.value is a Member of CrossRef Society for Industrial and Applied Mathematics

ARTICLE DATA

History
Received December 27, 2007
Accepted June 16, 2009
Published online September 02, 2009
Permalink
http://dx.doi.org/10.1137/070711761

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