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Parameterised integer programming, integer cones, and related problems
Cutting Stock Problem
Introduction
Introduction
Outline
Preliminaries
Basic definitions and notation
Matrices and linear algebra
Algorithms and complexity
Polyhedra and linear programming
The ellipsoid method
Integer programming and lattices
Integral Vectors in a Parameterised Polyhedron
Integer programming in fixed dimension
Lattice width of a parameterised polyhedron
Integer projections
Structural theorem
Application of the Structural Theorem
Parameterised integer programming
Integer programming gaps
Integer Programs in Standard Form
Carathéodory-type theorems
Integer programming problems in standard form
Cutting Stock Problem
Introduction
Integer programming formulation
Residual instances and small items
Integer programming gaps
Polynomial-size integer programs
Conclusions and Open Questions
Open problems
Dissertation
Parameterised integer programming, integer cones, and related problems / Gennady Shmonin
Entstehung
2007
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