Simultaneous Embedding of Two Paths on the Grid
Computational Geometry
2026-03-11 v1
Abstract
We study the problem of simultaneous geometric embedding of two paths without self-intersections on an integer grid. We show that minimizing the length of the longest edge of such an embedding is NP-hard. We also show that we can minimize in time the perimeter of an integer grid containing such an embedding if one path is -monotone and the other is -monotone.
Cite
@article{arxiv.2603.09750,
title = {Simultaneous Embedding of Two Paths on the Grid},
author = {Stephen Kobourov and William Lenhart and Giuseppe Liotta and Daniel Perz and Pavel Valtr and Johannes Zink},
journal= {arXiv preprint arXiv:2603.09750},
year = {2026}
}
Comments
Appears in the Proceedings of the 42nd European Workshop on Computational Geometry (EuroCG 2026)