Integer solutions for systems of linear inequalities, equations, and congruences are considered along with the construction and theoretical analysis of integer programming algorithms. The complexity of algorithms is analyzed dependent upon two parameters: the dimension, and the maximal modulus of the coefficients describing the conditions of the problem. The analysis is based on a thorough treatment of the qualitative and quantitative aspects of integer programming, in particular on bounds obtained by the author for the number of extreme points. This permits progress in many cases in which the traditional approach--which regards complexity as a function only of the length of the input--leads to a negative result.
Readership: Graduate students studying cybernetics and information science and applied mathematicians interested in the theory and applications of discrete optimization.
Author(s): V. N. Shevchenko
Series: Translations of Mathematical Monographs, Vol. 156
Publisher: American Mathematical Society
Year: 1996
Language: English
Pages: C, xiv+146, B
Intersection of a convex polyhedral cone with the integer lattice
A discrete analogue of the Farkas theorem, and the problem of aggregation of a system of linear integer equations
Intersection of a convex polyhedral set with the integer lattice
Cut methods in integer programming
Complexity questions in integer linear programming
Appendices
Bibliography
