{"year":"2026","has_accepted_license":"1","scopus_import":"1","title":"Cutting planarians: Planar emulators for string graphs","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"publisher":"Association for Computing Machinery","abstract":[{"lang":"eng","text":"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+ε 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 δG(u,v) ≤ δH(u,v) ≤ O(1) · δG(u,v). Furthermore, we show that for any constant ε > 0, there is an edge-weighted planar graph H′ such that every pair of vertices (u,v) satisfies δG(u,v) ≤ δH′(u,v) ≤ (1+ε) · δG(u,v) + O(ε−4polylogn). No previous constructions of sparse distance sketches were known even for intersection graphs of simple shapes like axis-parallel rectangles or fat convex polygons.\r\nAs applications, we construct the first (1+ε, +O(1)) mixed-distortion tree cover and distance oracle for arbitrary string graphs, as well as the first additive +(εΔ+O(1))-distortion embedding of string graphs G with diameter Δ into graphs of constant treewidth O(ε−4)."}],"month":"06","citation":{"short":"H.C. Chang, J. Conroy, Z. Tan, D.W. Zheng, in:, 58th Annual ACM Symposium on Theory of Computing, Association for Computing Machinery, 2026, pp. 2140–2151.","chicago":"Chang, Hsien Chih, Jonathan Conroy, Zihan Tan, and Da Wei Zheng. “Cutting Planarians: Planar Emulators for String Graphs.” In <i>58th Annual ACM Symposium on Theory of Computing</i>, 2140–51. Association for Computing Machinery, 2026. <a href=\"https://doi.org/10.1145/3798129.3800917\">https://doi.org/10.1145/3798129.3800917</a>.","ista":"Chang HC, Conroy J, Tan Z, Zheng DW. 2026. Cutting planarians: Planar emulators for string graphs. 58th Annual ACM Symposium on Theory of Computing. STOC: Symposium on the Theory of Computing, 2140–2151.","ama":"Chang HC, Conroy J, Tan Z, Zheng DW. Cutting planarians: Planar emulators for string graphs. In: <i>58th Annual ACM Symposium on Theory of Computing</i>. Association for Computing Machinery; 2026:2140-2151. doi:<a href=\"https://doi.org/10.1145/3798129.3800917\">10.1145/3798129.3800917</a>","mla":"Chang, Hsien Chih, et al. “Cutting Planarians: Planar Emulators for String Graphs.” <i>58th Annual ACM Symposium on Theory of Computing</i>, Association for Computing Machinery, 2026, pp. 2140–51, doi:<a href=\"https://doi.org/10.1145/3798129.3800917\">10.1145/3798129.3800917</a>.","ieee":"H. C. Chang, J. Conroy, Z. Tan, and D. W. Zheng, “Cutting planarians: Planar emulators for string graphs,” in <i>58th Annual ACM Symposium on Theory of Computing</i>, Salt Lake City, UT, United States, 2026, pp. 2140–2151.","apa":"Chang, H. C., Conroy, J., Tan, Z., &#38; Zheng, D. W. (2026). Cutting planarians: Planar emulators for string graphs. In <i>58th Annual ACM Symposium on Theory of Computing</i> (pp. 2140–2151). Salt Lake City, UT, United States: Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3798129.3800917\">https://doi.org/10.1145/3798129.3800917</a>"},"status":"public","das_tickbox":"0","date_created":"2026-07-05T22:01:37Z","OA_place":"publisher","doi":"10.1145/3798129.3800917","language":[{"iso":"eng"}],"_id":"22246","article_processing_charge":"No","quality_controlled":"1","ddc":["500","000"],"conference":{"location":"Salt Lake City, UT, United States","start_date":"2026-06-22","name":"STOC: Symposium on the Theory of Computing","end_date":"2026-06-26"},"OA_type":"gold","external_id":{"arxiv":["2510.21700"]},"oa":1,"publication":"58th Annual ACM Symposium on Theory of Computing","acknowledgement":"Hsien-Chih Chang and Jonathan Conroy are supported by the U.S.\r\nNational Science Foundation CAREER Award under the Grant No.\r\nCCF-2443017.","date_updated":"2026-07-06T10:25:23Z","corr_author":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","researchdata_availability":"no","author":[{"first_name":"Hsien Chih","full_name":"Chang, Hsien Chih","last_name":"Chang"},{"last_name":"Conroy","full_name":"Conroy, Jonathan","first_name":"Jonathan"},{"last_name":"Tan","full_name":"Tan, Zihan","first_name":"Zihan"},{"last_name":"Zheng","id":"af77956b-e859-11ef-8dc9-d301b898e32f","full_name":"Zheng, Da Wei","first_name":"Da Wei"}],"publication_identifier":{"isbn":["9798400725364"],"issn":["0737-8017"]},"arxiv":1,"oa_version":"Published Version","supplementarymaterial":"no","file":[{"checksum":"c184596a3e18fee912caef4c7751a96d","creator":"dernst","content_type":"application/pdf","file_id":"22253","access_level":"open_access","file_size":2015699,"file_name":"2026_STOC_Chang.pdf","relation":"main_file","date_updated":"2026-07-06T10:23:09Z","date_created":"2026-07-06T10:23:09Z","success":1}],"publication_status":"published","date_published":"2026-06-09T00:00:00Z","department":[{"_id":"MoHe"}],"page":"2140-2151","type":"conference","file_date_updated":"2026-07-06T10:23:09Z","day":"09"}