Voronoi-Based Similarity Distances between Arbitrary Crystal Lattices

Voronoi Cells of Lattices with Respect to Arbitrary Norms

Motivated by the deterministic single exponential time algorithm of Micciancio and Voulgaris for solving the shortest and closest vector problem for the Euclidean norm, we study the geometry and complexity of Voronoi cells of lattices with respect to arbitrary norms. On the positive side, we show that for strictly convex and smooth norms the geometry of Voronoi cells of lattices in any dimensio...

Computing Similarity Distances Between Rankings

We address the problem of computing distances between permutations that take into account similarities between elements of the ground set dictated by a graph. The problem may be summarized as follows: Given two permutations and a positive cost function on transpositions that depends on the similarity of the elements involved, find a smallest cost sequence of transpositions that converts one per...

Lattices with Few Distances*

The n-dimensional lattices that contain fewest distances are characterized for all n ≠ 2. ___________* This paper appeared in J. Number Theory, 39 (1991), 75-90. It is also DIMACS Technical Report 90-77,December 1990.

Similarity and Affine Invariant Distances Between 2D Point Sets

Three-dimensional Random Voronoi Tessellations: From Cubic Crystal Lattices to Poisson Point Processes

We perturb the simple cubic (SC), body-centered cubic (BCC), and face-centered cubic (FCC) structures with a spatial Gaussian noise whose adimensional strength is controlled by the parameter α and analyze the statistical properties of the cells of the resulting Voronoi tessellations. We concentrate on topological properties, such as the number of faces, and on metric properties, such as the are...