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Parameterised integer programming, integer cones, and related problems
Integral Vectors in a Parameterised Polyhedron
Lattice width of a parameterised polyhedron
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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