**Translations of Mathematical Monographs**

1997;
146 pp;
Hardcover

MSC: Primary 90;
Secondary 68

**Print ISBN: 978-0-8218-0535-0
Product Code: MMONO/156**

List Price: $82.00

Individual Member Price: $65.60

# Qualitative Topics in Integer Linear Programming

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*V. N. Shevchenko*

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.

#### Table of Contents

# Table of Contents

## Qualitative Topics in Integer Linear Programming

#### 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