Description
Book SynopsisTheory of Linear and Integer Programming Alexander Schrijver Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands This book describes the theory of linear and integer programming and surveys the algorithms for linear and integer programming problems, focusing on complexity analysis.
Trade Review"...a comprehensive exposition of the theory of linear and integer programming...complementing the more practically oriented books." (Zentralblatt MATH, Vol. 970, 2001/20)
Table of ContentsIntroduction and Preliminaries.
Problems, Algorithms, and Complexity.
LINEAR ALGEBRA.
Linear Algebra and Complexity.
LATTICES AND LINEAR DIOPHANTINE EQUATIONS.
Theory of Lattices and Linear Diophantine Equations.
Algorithms for Linear Diophantine Equations.
Diophantine Approximation and Basis Reduction.
POLYHEDRA, LINEAR INEQUALITIES, AND LINEAR PROGRAMMING.
Fundamental Concepts and Results on Polyhedra, Linear Inequalities, and Linear Programming.
The Structure of Polyhedra.
Polarity, and Blocking and Anti-Blocking Polyhedra.
Sizes and the Theoretical Complexity of Linear Inequalities and Linear Programming.
The Simplex Method.
Primal-Dual, Elimination, and Relaxation Methods.
Khachiyan's Method for Linear Programming.
The Ellipsoid Method for Polyhedra More Generally.
Further Polynomiality Results in Linear Programming.
INTEGER LINEAR PROGRAMMING.
Introduction to Integer Linear Programming.
Estimates in Integer Linear Programming.
The Complexity of Integer Linear Programming.
Totally Unimodular Matrices: Fundamental Properties and Examples.
Recognizing Total Unimodularity.
Further Theory Related to Total Unimodularity.
Integral Polyhedra and Total Dual Integrality.
Cutting Planes.
Further Methods in Integer Linear Programming.
References.
Indexes.
