Polynomial time algorithms in the theory of linear diophantine equations

  • M. A. Frumkin
Section C Computability, Decidability & Arithmetic Complexity
Part of the Lecture Notes in Computer Science book series (LNCS, volume 56)


Time Complexity Polynomial Time Algorithm Integer Solution Integer Vector Integer Matrix 
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  1. 1.
    W.A.Blankinship. A new version of the Euclidian algorithm. Amer. Math. Monthly, v. 70(1967), No. 3.Google Scholar
  2. 2.
    J. Bond. Calculation the general solution of a linear diophantine equation. Amer. Math. Monthly, v.74(1971), No. 8.Google Scholar
  3. 3.
    I. Borosh, A.S. Fraenkel. Exact solution of linear equations with rational coefficients by congruence techniques. Math. Comp., v. 20 (1966), No. 93.Google Scholar
  4. 4.
    G.H. Bradly. Algorithm and bound for the gratest common divisor of n integers. Comm. of ACM, v. 3(1970) No. 7.Google Scholar
  5. 5.
    G.H. Bradly. Algorithms for Hermite and Smith normal matrices and linear diophantine equations. Math. Comp., v. 25(1971), No. 116.Google Scholar
  6. 6.
    J.W.S. Cassels. An Introduction to The Geometry of numbers. Springer-Verlag, 1959.Google Scholar
  7. 7.
    M.A. Frumkin. Application of modular arithmetic to the construction of algorithms of solving systems of linear equations. Soviet Math. Dokl., v. 17(1976), No.4.Google Scholar
  8. 8.
    М.А. Фрумкин. Алгоритмы решения систем илнейных уравнений в целых числах. сб. "Исследования по дискретной оптимизации", М. "Наука", 1976, 97–127.Google Scholar
  9. 9.
    М.А. Фрумкин. Алгоритм приведения целочисленной матрицы к треугольному виду со степенной сложностью вычислений. Экономика и мат. методы, т. XII (1976), No I.Google Scholar
  10. 10.
    T.C. Hu and R.D. Young. Integer programming and network flows. Addison-Wesley, Reading, Mass., 1969.Google Scholar
  11. 11.
    А.А. Вотяков, М.А. Фрумкин. Алгоритм нахождения общего целочисленного решения системы линейных диофантовых уравнений. сб. "Исследования по дискретной оптимизации", М. "Наука", 1976, 128–140.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1977

Authors and Affiliations

  • M. A. Frumkin
    • 1
  1. 1.Department of Applied Mathematics Central Economics Mathematical InstituteAcademy of Sciences of the USSRUSSR

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