# On the Lattice Distortion Problem

@article{Bennett2016OnTL, title={On the Lattice Distortion Problem}, author={Huck Bennett and Daniel Dadush and Noah Stephens-Davidowitz}, journal={ArXiv}, year={2016}, volume={abs/1605.03613} }

We introduce and study the \emph{Lattice Distortion Problem} (LDP). LDP asks how "similar" two lattices are. I.e., what is the minimal distortion of a linear bijection between the two lattices? LDP generalizes the Lattice Isomorphism Problem (the lattice analogue of Graph Isomorphism), which simply asks whether the minimal distortion is one.
As our first contribution, we show that the distortion between any two lattices is approximated up to a $n^{O(\log n)}$ factor by a simple function of… CONTINUE READING

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