| 1 Fractured Lattices, Integer Programming, and Diophantine Approximation ⋆ (2008) | |||||||||||||||
Abstract | |||||||||||||||
| Abstract. For a d-dimensional lattice Λ and a d-dimensional vector a we consider the sequence of point sets An: = { ia + x | x ∈ Λ, 0 ≤ i<n} for increasing values of n. For the values of n when a new shortest nonzero vector appears in An+1, thesetAnhas a structure of a perturbed lattice, i. e., each point is in some small neighborhood of a (unique) lattice. We use this structure for a recursive approach to finding best approximations in fixed dimensions, with applications to integer programming. | |||||||||||||||
Publication details | |||||||||||||||
| |||||||||||||||