Approximating minimum unsatisfiability of linear equations

Piotr Berman, Marek Karpinski

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

    18 Scopus citations


    We consider the following optimization problem: given a system of m linear equations in n variables over a certain field, a feasible solution is any assignment of values to the variables, and the minimized objective function is the number of equations that are not satisfied. For the case of the finite field GF[2], this problem is also known as the Nearest Codeword problem. In this note we show that for any constant c there exists a randomized polynomial time algorithm that approximates the above problem, called the Minimum Unsatisfiability of Linear Equations (Min-Unsatisfy for short), with n/(clogn) approximation ratio. Our results hold for any field in which systems of linear equations can be solved in polynomial time.

    Original languageEnglish (US)
    Title of host publicationProceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2002
    PublisherAssociation for Computing Machinery
    Number of pages3
    ISBN (Electronic)089871513X
    StatePublished - 2002
    Event13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2002 - San Francisco, United States
    Duration: Jan 6 2002Jan 8 2002

    Publication series

    NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms


    Other13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2002
    Country/TerritoryUnited States
    CitySan Francisco

    All Science Journal Classification (ASJC) codes

    • Software
    • General Mathematics


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