{"id":"https://openalex.org/W7160948572","doi":"https://doi.org/10.48550/arxiv.2605.10692","title":"Charting the Diameter Computation Landscape on Intersection Graphs in the Plane","display_name":"Charting the Diameter Computation Landscape on Intersection Graphs in the Plane","publication_year":2026,"publication_date":"2026-05-11","ids":{"openalex":"https://openalex.org/W7160948572","doi":"https://doi.org/10.48550/arxiv.2605.10692"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.10692","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.10692","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.10692","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135935877","display_name":"Timothy C. Y. Chan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chan, Timothy M.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135991855","display_name":"Hsien-Chih Chang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chang, Hsien-Chih","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135951603","display_name":"Jie Gao","orcid":"https://orcid.org/0000-0003-1317-2445"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gao, Jie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135977181","display_name":"S\u00e1ndor Kisfaludi-Bak","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kisfaludi-Bak, S\u00e1ndor","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135941354","display_name":"Hung Le","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Le, Hung","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5135944770","display_name":"Da Wei Zheng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zheng, Da Wei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9524999856948853,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9524999856948853,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.00860000029206276,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.007699999958276749,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.6804999709129333},{"id":"https://openalex.org/keywords/intersection-graph","display_name":"Intersection graph","score":0.6473000049591064},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5490999817848206},{"id":"https://openalex.org/keywords/line-segment","display_name":"Line segment","score":0.5027999877929688},{"id":"https://openalex.org/keywords/equilateral-triangle","display_name":"Equilateral triangle","score":0.48559999465942383},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.47279998660087585},{"id":"https://openalex.org/keywords/computational-geometry","display_name":"Computational geometry","score":0.4571000039577484},{"id":"https://openalex.org/keywords/treewidth","display_name":"Treewidth","score":0.45080000162124634},{"id":"https://openalex.org/keywords/collision-detection","display_name":"Collision detection","score":0.4372999966144562}],"concepts":[{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.6804999709129333},{"id":"https://openalex.org/C54540088","wikidata":"https://www.wikidata.org/wiki/Q3498041","display_name":"Intersection graph","level":4,"score":0.6473000049591064},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5705000162124634},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5490999817848206},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5394999980926514},{"id":"https://openalex.org/C182124507","wikidata":"https://www.wikidata.org/wiki/Q166154","display_name":"Line segment","level":2,"score":0.5027999877929688},{"id":"https://openalex.org/C146786541","wikidata":"https://www.wikidata.org/wiki/Q157002","display_name":"Equilateral triangle","level":2,"score":0.48559999465942383},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.47279998660087585},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.4571000039577484},{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.45080000162124634},{"id":"https://openalex.org/C199668693","wikidata":"https://www.wikidata.org/wiki/Q1550329","display_name":"Collision detection","level":3,"score":0.4372999966144562},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4287000000476837},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.4269999861717224},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.41920000314712524},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4185999929904938},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4178999960422516},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40720000863075256},{"id":"https://openalex.org/C2781238097","wikidata":"https://www.wikidata.org/wiki/Q175026","display_name":"Object (grammar)","level":2,"score":0.39820000529289246},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.397599995136261},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3855000138282776},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.3644999861717224},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.3529999852180481},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.32659998536109924},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3138999938964844},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3118000030517578},{"id":"https://openalex.org/C130184317","wikidata":"https://www.wikidata.org/wiki/Q3115549","display_name":"Unit disk graph","level":4,"score":0.29089999198913574},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.28929999470710754},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.28360000252723694},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.28060001134872437},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.2667999863624573},{"id":"https://openalex.org/C84316537","wikidata":"https://www.wikidata.org/wiki/Q36255","display_name":"Unit vector","level":2,"score":0.265500009059906},{"id":"https://openalex.org/C3018263672","wikidata":"https://www.wikidata.org/wiki/Q1296251","display_name":"Efficient algorithm","level":2,"score":0.25609999895095825}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.10692","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.10692","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.10692","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.10692","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[{"score":0.5411856174468994,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Computing":[0],"the":[1,4,20,24,29,39,76,88,106,111,119,122,128,138,169,173,186,227,240,250],"diameter":[2,25,89,124,144,188,228,251,280],"of":[3,7,22,86,90,97,113,118,145,198,229,252,255],"intersection":[5,92,253],"graphs":[6,93,197,254],"objects":[8,129],"is":[9,41,69,108,115,189,216,233,261,265,281],"a":[10,83,116,179,212,230],"basic":[11],"problem":[12,40],"in":[13,37,43,57,66,153],"computational":[14],"geometry.":[15],"Previous":[16,157,201,272],"works":[17],"showed":[18],"that":[19,105,178],"complexity":[21,270],"computing":[23,87],"mainly":[26],"depends":[27],"on":[28,204],"object":[30,120],"types:":[31],"for":[32,48,94,137,160,172,195,210],"unit":[33,52,60,64],"disks":[34],"and":[35,54,62,126],"squares":[36],"2D,":[38],"solvable":[42],"truly":[44,71,154,180,266],"subquadratic":[45,72,155,181],"time,":[46],"while":[47],"other":[49,170],"objects,":[50],"including":[51],"segments":[53,149,162,260],"equilateral":[55],"triangles":[56,257],"2D":[58,139],"or":[59,258],"balls":[61],"axis-parallel":[63],"cubes":[65],"3D,":[67],"there":[68],"no":[70],"time":[73,182,215,245],"algorithm":[74,183,194,223,242],"under":[75,268],"Orthogonal":[77],"Vector":[78],"(OV)":[79],"hypothesis.":[80],"We":[81,99],"undertake":[82],"comprehensive":[84],"study":[85],"geometric":[91],"various":[95],"types":[96],"objects.":[98],"discover":[100],"many":[101],"new":[102],"irregularities,":[103],"showing":[104],"landscape":[107],"extremely":[109],"nuanced:":[110],"source":[112],"hardness":[114,158],"combination":[117],"type,":[121],"true":[123,187],"value,":[125],"how":[127],"intersect":[130],"with":[131,243],"each":[132],"other.":[133],"Our":[134],"highlighted":[135],"results":[136],"case":[140],"include:":[141],"1.":[142],"The":[143],"non-degenerate,":[146],"axis-aligned":[147],"line":[148,161,259],"can":[150],"be":[151],"computed":[152],"time.":[156],"result":[159],"applies":[163],"only":[164,275],"to":[165,224],"degenerate":[166,174],"instances.":[167],"On":[168],"hand,":[171],"case,":[175],"we":[176],"show":[177],"exists":[184],"when":[185,277],"constant.":[190],"2.":[191,236],"An":[192,221],"almost-linear-time":[193],"unit-square":[196],"constant":[199],"diameter.":[200],"algorithms":[202],"rely":[203],"succinct":[205],"representation":[206],"assuming":[207],"bounded":[208],"VC-dimension;":[209],"such":[211],"strategy":[213],"$\u03a9(n^{7/4})$":[214],"an":[217],"inherent":[218],"barrier.":[219],"3.":[220,284],"$\\tilde{O}(n^{4/3})$-time":[222],"decide":[225],"if":[226,249,279],"unit-disk":[231],"graph":[232],"at":[234,262,282],"most":[235,263,283],"This":[237],"improves":[238],"upon":[239],"recent":[241],"running":[244],"$\\tilde{O}(n^{2-1/9})$.":[246],"4.":[247],"Deciding":[248],"fat":[256],"2":[264],"subquadratic-hard":[267],"fine-grained":[269],"assumptions.":[271],"lower":[273],"bounds":[274],"hold":[276],"deciding":[278]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-05-13T00:00:00"}