论文信息 - Integer Programming with a Fixed Number of Variables - 字舞流文

Integer Programming with a Fixed Number of Variables

It is shown that the integer linear programming problem with a fixed number of variables is polynomially solvable. The proof depends on methods from geometry of numbers.

Hendrik W. Lenstra | H. Lenstra

[1] B. L. Waerden. Die Reduktionstheorie Der Positiven Quadratischen Formen , 1956 .

[2] C. A. Rogers,et al. An Introduction to the Geometry of Numbers , 1959 .

[3] J. Edmonds. Systems of distinct representatives and linear algebra , 1967 .

[4] Chak-Kuen Wong,et al. A Polynomial-Time Algorithm for the Knapsack Problem with Two Variables , 1976, JACM.

[5] J. Gathen,et al. A bound on solutions of linear integer equalities and inequalities , 1978 .

[6] David S. Johnson,et al. Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[7] L. G. H. Cijan. A polynomial algorithm in linear programming , 1979 .

[8] Ravi Kannan,et al. Polynomial Algorithms for Computing the Smith and Hermite Normal Forms of an Integer Matrix , 1979, SIAM J. Comput..

[9] Ravi Kannan,et al. A Polynomial Algorithm for the Two-Variable Integer Programming Problem , 1980, JACM.

[10] L. Khachiyan. Polynomial algorithms in linear programming , 1980 .

[11] H. Scarf. Production Sets with Indivisibilities Part I: Generalities , 1981 .

[12] Martin Grötschel,et al. The ellipsoid method and its consequences in combinatorial optimization , 1981, Comb..

[13] László Lovász,et al. Factoring polynomials with rational coefficients , 1982 .