Faster integer multiplication

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    106 Citations (Scopus)

    Abstract

    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.

    Original languageEnglish (US)
    Title of host publicationSTOC'07
    Subtitle of host publicationProceedings of the 39th Annual ACM Symposium on Theory of Computing
    Pages57-66
    Number of pages10
    DOIs
    StatePublished - Oct 30 2007
    EventSTOC'07: 39th Annual ACM Symposium on Theory of Computing - San Diego, CA, United States
    Duration: Jun 11 2007Jun 13 2007

    Publication series

    NameProceedings of the Annual ACM Symposium on Theory of Computing
    ISSN (Print)0737-8017

    Other

    OtherSTOC'07: 39th Annual ACM Symposium on Theory of Computing
    CountryUnited States
    CitySan Diego, CA
    Period6/11/076/13/07

    Fingerprint

    Turing machines
    Networks (circuits)

    All Science Journal Classification (ASJC) codes

    • Software

    Cite this

    Furer, M. (2007). Faster integer multiplication. In STOC'07: Proceedings of the 39th Annual ACM Symposium on Theory of Computing (pp. 57-66). (Proceedings of the Annual ACM Symposium on Theory of Computing). https://doi.org/10.1145/1250790.1250800
    Furer, Martin. / Faster integer multiplication. STOC'07: Proceedings of the 39th Annual ACM Symposium on Theory of Computing. 2007. pp. 57-66 (Proceedings of the Annual ACM Symposium on Theory of Computing).
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    Furer, M 2007, Faster integer multiplication. in STOC'07: Proceedings of the 39th Annual ACM Symposium on Theory of Computing. Proceedings of the Annual ACM Symposium on Theory of Computing, pp. 57-66, STOC'07: 39th Annual ACM Symposium on Theory of Computing, San Diego, CA, United States, 6/11/07. https://doi.org/10.1145/1250790.1250800

    Faster integer multiplication. / Furer, Martin.

    STOC'07: Proceedings of the 39th Annual ACM Symposium on Theory of Computing. 2007. p. 57-66 (Proceedings of the Annual ACM Symposium on Theory of Computing).

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

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    Furer M. Faster integer multiplication. In STOC'07: Proceedings of the 39th Annual ACM Symposium on Theory of Computing. 2007. p. 57-66. (Proceedings of the Annual ACM Symposium on Theory of Computing). https://doi.org/10.1145/1250790.1250800