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.

Reviews

"Of interest ... references many papers in Russian that are largely unavailable outside (and, sometimes, inside) Russia."

-- Mathematical Reviews

Table of Contents

• 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