English

O(1)-Distortion Planar Emulators for String Graphs

Data Structures and Algorithms 2025-10-27 v1 Computational Geometry Discrete Mathematics Combinatorics Metric Geometry

Abstract

We show that every unweighted string graph GG has an O(1)O(1)-distortion planar emulator: that is, there exists an (edge-weighted) planar graph HH with V(H)=V(G)V(H) = V(G), such that every pair of vertices (u,v)(u,v) satisfies δG(u,v)δH(u,v)O(1)δG(u,v).\delta_G(u,v) \le \delta_H(u,v) \le O(1) \cdot \delta_G(u,v).

Keywords

Cite

@article{arxiv.2510.21700,
  title  = {O(1)-Distortion Planar Emulators for String Graphs},
  author = {Hsien-Chih Chang and Jonathan Conroy and Zihan Tan and Da Wei Zheng},
  journal= {arXiv preprint arXiv:2510.21700},
  year   = {2025}
}
R2 v1 2026-07-01T07:04:25.833Z