{"ID":2850799,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.21700","arxiv_id":"2510.21700","title":"O(1)-Distortion Planar Emulators for String Graphs","abstract":"We show that every unweighted string graph $G$ has an $O(1)$-distortion planar emulator: that is, there exists an (edge-weighted) planar graph $H$ with $V(H) = V(G)$, such that every pair of vertices $(u,v)$ satisfies $δ_G(u,v) \\le δ_H(u,v) \\le O(1) \\cdot δ_G(u,v).$","short_abstract":"We show that every unweighted string graph $G$ has an $O(1)$-distortion planar emulator: that is, there exists an (edge-weighted) planar graph $H$ with $V(H) = V(G)$, such that every pair of vertices $(u,v)$ satisfies $δ_G(u,v) \\le δ_H(u,v) \\le O(1) \\cdot δ_G(u,v).$","url_abs":"https://arxiv.org/abs/2510.21700","url_pdf":"https://arxiv.org/pdf/2510.21700v1","authors":"[\"Hsien-Chih Chang\",\"Jonathan Conroy\",\"Zihan Tan\",\"Da Wei Zheng\"]","published":"2025-10-24T17:58:03Z","proceeding":"cs.DS","tasks":"[\"cs.DS\",\"cs.CG\",\"cs.DM\",\"math.CO\",\"math.MG\"]","methods":"[]","has_code":false}