Discrete Tomography pp 35-58 | Cite as

# Sets of Uniqueness and Additivity in Integer Lattices

Chapter

## Abstract

A mathematical formulation is provided for inversion problems in which local structures of finite subsets of integer lattices are to be deduced from point counts in prescribed linear manifolds of an n-dimensional space. Notions of uniqueness and additivity for finite lattice sets are defined and characterized by point configurations and by aspects of fractional subsets of the lattice. The latter feature leads to analysis by interior point linear programming, which appears to be a very effective as well as efficient approximation approach to discrete inversion problems.

## Keywords

Interior Point Method Extreme Solution Linear Manifold Integer Lattice Linear Programming Approach
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© Springer Science+Business Media New York 1999