{"corr_author":"1","acknowledgement":"Timothy M. Chan: Supported by NSF grant CCF-2224271.\r\nHsien-Chih Chang: Supported by NSF CAREER award CCF-2443017.\r\nJie Gao: Supported by NSF DMS-2220271, DMS-2311064, IIS-2229876, CCF-2118953, CNS-2515159.\r\nSándor Kisfaludi-Bak: Supported by the Research Council of Finland, Grant 363444.\r\nHung Le: Supported by an NSF grant CCF-2517033 and an NSF CAREER Award CCF-2237288.\r\nDa Wei Zheng: This project has received funding from the Austrian Science Fund (FWF) grant\r\nDOI 10.55776/I5982. For open access purposes, the author has applied a CC BY public copyright\r\nlicense to any author-accepted manuscript version arising from this submission.\r\n","date_updated":"2026-07-27T06:22:03Z","publication":"53rd International Colloquium on Automata, Languages, and Programming","supplementarymaterial":"no","article_number":"54:1-54:22","arxiv":1,"oa_version":"Published Version","publication_identifier":{"eissn":["1868-8969","9783959774284"]},"author":[{"first_name":"Timothy M.","full_name":"Chan, Timothy M.","last_name":"Chan","orcid":"0000-0002-8093-0675"},{"orcid":"0000-0001-6714-7988","last_name":"Chang","first_name":"Hsien-Chih","full_name":"Chang, Hsien-Chih"},{"last_name":"Gao","orcid":"0000-0001-5083-6082","first_name":"Jie","full_name":"Gao, Jie"},{"orcid":"0000-0002-6856-2902","last_name":"Kisfaludi-Bak","first_name":"Sándor","full_name":"Kisfaludi-Bak, Sándor"},{"last_name":"Le","orcid":"0000-0001-8223-9944","first_name":"Hung","full_name":"Le, Hung"},{"last_name":"Zheng","id":"af77956b-e859-11ef-8dc9-d301b898e32f","first_name":"Da Wei","full_name":"Zheng, Da Wei"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","researchdata_availability":"no","publication_status":"published","file":[{"success":1,"date_created":"2026-07-27T06:20:41Z","date_updated":"2026-07-27T06:20:41Z","relation":"main_file","file_name":"2026_LIPIcSICALP_Chan.pdf","access_level":"open_access","file_size":1440497,"creator":"dernst","checksum":"1e66eba4cfe4e74ab28108b1ca0bb956","content_type":"application/pdf","file_id":"22407"}],"intvolume":"       374","day":"01","file_date_updated":"2026-07-27T06:20:41Z","department":[{"_id":"MoHe"}],"type":"conference","date_published":"2026-07-01T00:00:00Z","has_accepted_license":"1","year":"2026","scopus_import":"1","license":"https://creativecommons.org/licenses/by/4.0/","abstract":[{"text":"Computing the diameter of the intersection graphs of objects is a basic problem in computational geometry. Previous works showed that the complexity of computing the diameter mainly depends on the object types: for unit disks and squares in 2D, the problem is solvable in truly subquadratic time [Chan et al., 2025], while for other objects, including unit segments and equilateral triangles in 2D or unit balls and axis-parallel unit cubes in 3D, there is no truly subquadratic time algorithm under the Orthogonal Vector (OV) hypothesis [Bringmann et al., 2022]. \r\nWe undertake a comprehensive study of computing the diameter of geometric intersection graphs for various types of objects. We discover many new irregularities, showing that the landscape is extremely nuanced: the source of hardness is a combination of the object type, the true diameter value, and how the objects intersect with each other. Our highlighted results for the 2D case include:  \r\n1) The diameter of non-degenerate, axis-aligned line segments can be computed in truly subquadratic time. Previous hardness result [Bringmann et al., 2022] for line segments applies only to degenerate instances. On the other hand, for the degenerate case, we show that a truly subquadratic time algorithm exists when the true diameter is constant. \r\n2) An almost-linear-time algorithm for unit-square graphs of constant diameter. Previous algorithms [Duraj et al., 2024; Chan et al., 2025] rely on succinct representation assuming bounded VC-dimension; for such a strategy Ω(n^{7/4}) time is an inherent barrier. \r\n3) An Õ(n^{4/3})-time algorithm to decide if the diameter of a unit-disk graph is at most 2. This improves upon the recent algorithm with running time Õ(n^{2-1/9}) [Chan et al., 2025]. \r\n4) Deciding if the diameter of intersection graphs of fat triangles or line segments is at most 2 is truly subquadratic-hard under fine-grained complexity assumptions. Previous lower bounds [Bringmann et al., 2022] only hold when deciding if diameter is at most 3.  Our findings are presented in a pair of papers. This paper focuses solely on the 2D case, while the companion paper is devoted to higher-dimensional cases.","lang":"eng"}],"keyword":["String graphs","Fine-grained complexity","Theory of computation → Computational geometry"],"publisher":"Schloss Dagstuhl – Leibniz-Zentrum für Informatik","title":"Charting the landscape of diameter computation on geometric intersection graphs in the plane","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)"},"volume":374,"language":[{"iso":"eng"}],"OA_place":"publisher","doi":"10.4230/LIPICS.ICALP.2026.54","das_tickbox":"0","status":"public","date_created":"2026-07-27T05:53:08Z","project":[{"name":"Static and Dynamic Hierarchical Graph Decompositions","_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103","grant_number":"I05982"}],"month":"07","citation":{"apa":"Chan, T. M., Chang, H.-C., Gao, J., Kisfaludi-Bak, S., Le, H., &#38; Zheng, D. W. (2026). Charting the landscape of diameter computation on geometric intersection graphs in the plane. In <i>53rd International Colloquium on Automata, Languages, and Programming</i> (Vol. 374). Egham, United Kingdom: Schloss Dagstuhl – Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPICS.ICALP.2026.54\">https://doi.org/10.4230/LIPICS.ICALP.2026.54</a>","ama":"Chan TM, Chang H-C, Gao J, Kisfaludi-Bak S, Le H, Zheng DW. Charting the landscape of diameter computation on geometric intersection graphs in the plane. In: <i>53rd International Colloquium on Automata, Languages, and Programming</i>. Vol 374. Schloss Dagstuhl – Leibniz-Zentrum für Informatik; 2026. doi:<a href=\"https://doi.org/10.4230/LIPICS.ICALP.2026.54\">10.4230/LIPICS.ICALP.2026.54</a>","ieee":"T. M. Chan, H.-C. Chang, J. Gao, S. Kisfaludi-Bak, H. Le, and D. W. Zheng, “Charting the landscape of diameter computation on geometric intersection graphs in the plane,” in <i>53rd International Colloquium on Automata, Languages, and Programming</i>, Egham, United Kingdom, 2026, vol. 374.","mla":"Chan, Timothy M., et al. “Charting the Landscape of Diameter Computation on Geometric Intersection Graphs in the Plane.” <i>53rd International Colloquium on Automata, Languages, and Programming</i>, vol. 374, 54:1-54:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik, 2026, doi:<a href=\"https://doi.org/10.4230/LIPICS.ICALP.2026.54\">10.4230/LIPICS.ICALP.2026.54</a>.","ista":"Chan TM, Chang H-C, Gao J, Kisfaludi-Bak S, Le H, Zheng DW. 2026. Charting the landscape of diameter computation on geometric intersection graphs in the plane. 53rd International Colloquium on Automata, Languages, and Programming. ICALP: Automata, Languages and Programming vol. 374, 54:1-54:22.","chicago":"Chan, Timothy M., Hsien-Chih Chang, Jie Gao, Sándor Kisfaludi-Bak, Hung Le, and Da Wei Zheng. “Charting the Landscape of Diameter Computation on Geometric Intersection Graphs in the Plane.” In <i>53rd International Colloquium on Automata, Languages, and Programming</i>, Vol. 374. Schloss Dagstuhl – Leibniz-Zentrum für Informatik, 2026. <a href=\"https://doi.org/10.4230/LIPICS.ICALP.2026.54\">https://doi.org/10.4230/LIPICS.ICALP.2026.54</a>.","short":"T.M. Chan, H.-C. Chang, J. Gao, S. Kisfaludi-Bak, H. Le, D.W. Zheng, in:, 53rd International Colloquium on Automata, Languages, and Programming, Schloss Dagstuhl – Leibniz-Zentrum für Informatik, 2026."},"oa":1,"conference":{"location":"Egham, United Kingdom","end_date":"2026-07-10","name":"ICALP: Automata, Languages and Programming","start_date":"2026-07-07"},"OA_type":"gold","external_id":{"arxiv":["2605.10692"]},"ddc":["000"],"_id":"22405","quality_controlled":"1","article_processing_charge":"No"}