Approximating permanents of complex matrices

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

    2 Citations (Scopus)

    Abstract

    A wide variety of approximation algorithms for permanents of non-negative matrices has been proposed and analyzed before [5; 7; 9; 1]. Usually, these approximation algorithms have been presented for 0-1 matrices and it has been remarked that they extend to other matrices as long as all entries are non-negative. Here we present the first approximation algorithm for the permanent of an arbitrary complex matrix. We extend the notion of an (ε,δ)-approximation algorithm to accommodate for cancellations in additions. Our running time is Õ(3n/2 ε-2 log 1/δ) compared to Õ(2n/2 ε-2 log 1/δ) for non-negative matrices. (A faster algorithm is known for 0-1 matrices [6].).

    Original languageEnglish (US)
    Title of host publicationProceedings of the 32nd Annual ACM Symposium on Theory of Computing, STOC 2000
    Pages667-669
    Number of pages3
    DOIs
    StatePublished - Dec 1 2000
    Event32nd Annual ACM Symposium on Theory of Computing, STOC 2000 - Portland, OR, United States
    Duration: May 21 2000May 23 2000

    Publication series

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

    Conference

    Conference32nd Annual ACM Symposium on Theory of Computing, STOC 2000
    CountryUnited States
    CityPortland, OR
    Period5/21/005/23/00

    Fingerprint

    Approximation algorithms

    All Science Journal Classification (ASJC) codes

    • Software

    Cite this

    Furer, M. (2000). Approximating permanents of complex matrices. In Proceedings of the 32nd Annual ACM Symposium on Theory of Computing, STOC 2000 (pp. 667-669). (Proceedings of the Annual ACM Symposium on Theory of Computing). https://doi.org/10.1145/335305.335399
    Furer, Martin. / Approximating permanents of complex matrices. Proceedings of the 32nd Annual ACM Symposium on Theory of Computing, STOC 2000. 2000. pp. 667-669 (Proceedings of the Annual ACM Symposium on Theory of Computing).
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    abstract = "A wide variety of approximation algorithms for permanents of non-negative matrices has been proposed and analyzed before [5; 7; 9; 1]. Usually, these approximation algorithms have been presented for 0-1 matrices and it has been remarked that they extend to other matrices as long as all entries are non-negative. Here we present the first approximation algorithm for the permanent of an arbitrary complex matrix. We extend the notion of an (ε,δ)-approximation algorithm to accommodate for cancellations in additions. Our running time is {\~O}(3n/2 ε-2 log 1/δ) compared to {\~O}(2n/2 ε-2 log 1/δ) for non-negative matrices. (A faster algorithm is known for 0-1 matrices [6].).",
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    Furer, M 2000, Approximating permanents of complex matrices. in Proceedings of the 32nd Annual ACM Symposium on Theory of Computing, STOC 2000. Proceedings of the Annual ACM Symposium on Theory of Computing, pp. 667-669, 32nd Annual ACM Symposium on Theory of Computing, STOC 2000, Portland, OR, United States, 5/21/00. https://doi.org/10.1145/335305.335399

    Approximating permanents of complex matrices. / Furer, Martin.

    Proceedings of the 32nd Annual ACM Symposium on Theory of Computing, STOC 2000. 2000. p. 667-669 (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. Approximating permanents of complex matrices. In Proceedings of the 32nd Annual ACM Symposium on Theory of Computing, STOC 2000. 2000. p. 667-669. (Proceedings of the Annual ACM Symposium on Theory of Computing). https://doi.org/10.1145/335305.335399