Faster integer multiplication

For more than 35 years, the fastest known method for integer multiplication has been the Sch?onhage-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. All this time, the prevailing conjecture has been that the complexity of an optimal integer multiplication 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 2O(log n). The running time bound holds for multitape Turing machines. The same bound is valid for the size of boolean circuits.

• Type: Conference
• Year: 2007
• Where: STOC
• Authors: Martin Fürer
• Keywords: Algorithms, Log Log N, N Log N, STOC 2007, Time O(n Log