TY - GEN

T1 - Faster integer multiplication

AU - Fürer, Martin

PY - 2007

Y1 - 2007

N2 - 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 (n log n) lower bound. The prevailing conjecture has always been that the complexity of an optimal algorithm is (n log n). We present a major step towards closing the gap from above by presenting an algorithm running in time n log n, 2 O(log*n). The main result is for boolean circuits as well as for multitape Turing machines, but it has consequences to other models of computation as well.

AB - 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 (n log n) lower bound. The prevailing conjecture has always been that the complexity of an optimal algorithm is (n log n). We present a major step towards closing the gap from above by presenting an algorithm running in time n log n, 2 O(log*n). The main result is for boolean circuits as well as for multitape Turing machines, but it has consequences to other models of computation as well.

UR - http://www.scopus.com/inward/record.url?scp=35448968883&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35448968883&partnerID=8YFLogxK

U2 - 10.1145/1250790.1250800

DO - 10.1145/1250790.1250800

M3 - Conference contribution

AN - SCOPUS:35448968883

SN - 1595936319

SN - 9781595936318

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 57

EP - 66

BT - STOC'07

T2 - STOC'07: 39th Annual ACM Symposium on Theory of Computing

Y2 - 11 June 2007 through 13 June 2007

ER -