{"paper":{"title":"Cutting Planarians: Planar Emulators for String Graphs","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.CG","cs.DM","math.CO","math.MG"],"primary_cat":"cs.DS","authors_text":"Da Wei Zheng, Hsien-Chih Chang, Jonathan Conroy, Zihan Tan","submitted_at":"2025-10-24T17:58:03Z","abstract_excerpt":"In this paper we construct distance sketches for intersection graphs of arbitrary path-connected regions in the plane (known as the string graphs) in the constant and $1+\\varepsilon$ distortion regimes. Furthermore, the distance sketches themselves are planar graphs. First, we show that every unweighted string graph $G$ has an $O(1)$-distortion planar emulator: that is, there exists an edge-weighted planar graph $H$ containing every vertex in $G$, such that every pair of vertices $(u,v)$ satisfies $\\delta_G(u,v) \\le \\delta_H(u,v) \\le O(1) \\cdot \\delta_G(u,v)$. Furthermore, we show that for any"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.21700","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2510.21700/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}