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Qualitative Topics in Integer Linear Programming

V. N. Shevchenko Nizhnii Novgorod, Russia
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Hardcover ISBN: 978-0-8218-0535-0
Product Code: MMONO/156
List Price: $87.00 MAA Member Price:$78.30
AMS Member Price: $69.60 Electronic ISBN: 978-1-4704-4571-3 Product Code: MMONO/156.E List Price:$82.00
MAA Member Price: $73.80 AMS Member Price:$65.60
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List Price: $130.50 MAA Member Price:$117.45
AMS Member Price: $104.40 Click above image for expanded view Qualitative Topics in Integer Linear Programming V. N. Shevchenko Nizhnii Novgorod, Russia Available Formats:  Hardcover ISBN: 978-0-8218-0535-0 Product Code: MMONO/156  List Price:$87.00 MAA Member Price: $78.30 AMS Member Price:$69.60
 Electronic ISBN: 978-1-4704-4571-3 Product Code: MMONO/156.E
 List Price: $82.00 MAA Member Price:$73.80 AMS Member Price: $65.60 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$130.50 MAA Member Price: $117.45 AMS Member Price:$104.40
• Book Details

Translations of Mathematical Monographs
Volume: 1561997; 146 pp
MSC: Primary 90; Secondary 68;

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.

Graduate students studying cybernetics and information science and applied mathematicians interested in the theory and applications of discrete optimization.

• Chapters
• Chapter 1. Intersection of a convex polyhedral cone with the integer lattice
• Chapter 2. A discrete analogue of the Farkas theorem, and the problem of aggregation of a system of linear integer equations
• Chapter 3. Intersection of a convex polyhedral set with the integer lattice
• Chapter 4. Cut methods in integer programming
• Chapter 5. Complexity questions in integer linear programming
• Appendix 1. Solution of systems of linear equations and congruences in integers
• Appendix 2. Examples of applied problems related to the topic of the book
• Appendix 3. Investigation of minor and permanent characteristics of certain Boolean matrices
• Appendix 4. Threshold functions of many-valued logic and their deciphering
• Reviews

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

Mathematical Reviews
• Request Review Copy
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Volume: 1561997; 146 pp
MSC: Primary 90; Secondary 68;

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.

Graduate students studying cybernetics and information science and applied mathematicians interested in the theory and applications of discrete optimization.

• Chapters
• Chapter 1. Intersection of a convex polyhedral cone with the integer lattice
• Chapter 2. A discrete analogue of the Farkas theorem, and the problem of aggregation of a system of linear integer equations
• Chapter 3. Intersection of a convex polyhedral set with the integer lattice
• Chapter 4. Cut methods in integer programming
• Chapter 5. Complexity questions in integer linear programming
• Appendix 1. Solution of systems of linear equations and congruences in integers
• Appendix 2. Examples of applied problems related to the topic of the book
• Appendix 3. Investigation of minor and permanent characteristics of certain Boolean matrices
• Appendix 4. Threshold functions of many-valued logic and their deciphering
• Of interest … references many papers in Russian that are largely unavailable outside (and, sometimes, inside) Russia.

Mathematical Reviews
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