English

Drawing the double circle on a grid of minimum size

Computational Geometry 2013-05-30 v1 Combinatorics

Abstract

In 1926, Jarn\'ik introduced the problem of drawing a convex nn-gon with vertices having integer coordinates. He constructed such a drawing in the grid [1,cn3/2]2[1,c\cdot n^{3/2}]^2 for some constant c>0c>0, and showed that this grid size is optimal up to a constant factor. We consider the analogous problem for drawing the double circle, and prove that it can be done within the same grid size. Moreover, we give an O(n)-time algorithm to construct such a point set.

Cite

@article{arxiv.1305.6693,
  title  = {Drawing the double circle on a grid of minimum size},
  author = {Sergey Bereg and Ruy Fabila-Monroy and David Flores-Peñaloza and Mario Lopez and Pablo Pérez-Lantero},
  journal= {arXiv preprint arXiv:1305.6693},
  year   = {2013}
}
R2 v1 2026-06-22T00:24:18.442Z