{"id":"https://openalex.org/W7163894009","doi":"https://doi.org/10.4230/lipics.swat.2026.2","title":"On the Fragile Complexity of Geometric Algorithms","display_name":"On the Fragile Complexity of Geometric Algorithms","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7163894009","doi":"https://doi.org/10.4230/lipics.swat.2026.2"},"language":"en","primary_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:26038","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.2","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol370-swat2026/LIPIcs.SWAT.2026.2/LIPIcs.SWAT.2026.2.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"publishedVersion"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol370-swat2026/LIPIcs.SWAT.2026.2/LIPIcs.SWAT.2026.2.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5138119718","display_name":"Boris Aronov","orcid":"https://orcid.org/0000-0003-3110-4702"},"institutions":[{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Aronov, Boris","raw_affiliation_strings":["Department of Computer Science and Engineering, Tandon School of Engineering, New York University, Brooklyn, NY, USA"],"raw_orcid":"https://orcid.org/0000-0003-3110-4702","affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, Tandon School of Engineering, New York University, Brooklyn, NY, USA","institution_ids":["https://openalex.org/I57206974"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138142886","display_name":"Mayank Goswami","orcid":"https://orcid.org/0000-0002-2111-3210"},"institutions":[{"id":"https://openalex.org/I111455621","display_name":"Queens College, CUNY","ror":"https://ror.org/03v8adn41","country_code":"US","type":"education","lineage":["https://openalex.org/I111455621"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Goswami, Mayank","raw_affiliation_strings":["Department of Computer Science, Queens College CUNY, New York, NY, USA"],"raw_orcid":"https://orcid.org/0000-0002-2111-3210","affiliations":[{"raw_affiliation_string":"Department of Computer Science, Queens College CUNY, New York, NY, USA","institution_ids":["https://openalex.org/I111455621"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088852372","display_name":"John Iacono","orcid":"https://orcid.org/0000-0001-8885-8172"},"institutions":[{"id":"https://openalex.org/I132053463","display_name":"Universit\u00e9 Libre de Bruxelles","ror":"https://ror.org/01r9htc13","country_code":"BE","type":"education","lineage":["https://openalex.org/I132053463"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Iacono, John","raw_affiliation_strings":["Universit\u00e9 libre de Bruxelles, Ixelles, Belgium"],"raw_orcid":"https://orcid.org/0000-0001-8885-8172","affiliations":[{"raw_affiliation_string":"Universit\u00e9 libre de Bruxelles, Ixelles, Belgium","institution_ids":["https://openalex.org/I132053463"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5094087453","display_name":"Indu Ramesh","orcid":"https://orcid.org/0009-0008-9967-0819"},"institutions":[{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ramesh, Indu","raw_affiliation_strings":["Department of Computer Science and Engineering, Tandon School of Engineering, New York University, Brooklyn, NY, USA"],"raw_orcid":"https://orcid.org/0009-0008-9967-0819","affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, Tandon School of Engineering, New York University, Brooklyn, NY, USA","institution_ids":["https://openalex.org/I57206974"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.97243561,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"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":0.4936000108718872,"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":0.4936000108718872,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.10360000282526016,"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/T11106","display_name":"Data Management and Algorithms","score":0.08959999680519104,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/computational-complexity-theory","display_name":"Computational complexity theory","score":0.48559999465942383},{"id":"https://openalex.org/keywords/bounding-overwatch","display_name":"Bounding overwatch","score":0.48170000314712524},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.47920000553131104},{"id":"https://openalex.org/keywords/minimum-spanning-tree","display_name":"Minimum spanning tree","score":0.4740999937057495},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.4683000147342682},{"id":"https://openalex.org/keywords/computational-geometry","display_name":"Computational geometry","score":0.4625000059604645},{"id":"https://openalex.org/keywords/spanning-tree","display_name":"Spanning tree","score":0.45509999990463257},{"id":"https://openalex.org/keywords/sorting","display_name":"Sorting","score":0.45399999618530273},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.45329999923706055}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5566999912261963},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5559999942779541},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.48559999465942383},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.48170000314712524},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.47920000553131104},{"id":"https://openalex.org/C13743678","wikidata":"https://www.wikidata.org/wiki/Q240464","display_name":"Minimum spanning tree","level":2,"score":0.4740999937057495},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.4683000147342682},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.4625000059604645},{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.45509999990463257},{"id":"https://openalex.org/C111696304","wikidata":"https://www.wikidata.org/wiki/Q2303697","display_name":"Sorting","level":2,"score":0.45399999618530273},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.45329999923706055},{"id":"https://openalex.org/C135981907","wikidata":"https://www.wikidata.org/wiki/Q188056","display_name":"Triangulation","level":2,"score":0.4424999952316284},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.40869998931884766},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.39809998869895935},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36719998717308044},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.36719998717308044},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.33660000562667847},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3255999982357025},{"id":"https://openalex.org/C24404364","wikidata":"https://www.wikidata.org/wiki/Q7246846","display_name":"Probabilistic analysis of algorithms","level":3,"score":0.3188000023365021},{"id":"https://openalex.org/C164215192","wikidata":"https://www.wikidata.org/wiki/Q13414364","display_name":"Asymptotic computational complexity","level":4,"score":0.3125999867916107},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3116999864578247},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.29499998688697815},{"id":"https://openalex.org/C196921405","wikidata":"https://www.wikidata.org/wiki/Q786431","display_name":"Online algorithm","level":2,"score":0.29159998893737793},{"id":"https://openalex.org/C68010082","wikidata":"https://www.wikidata.org/wiki/Q192445","display_name":"Delaunay triangulation","level":2,"score":0.29120001196861267},{"id":"https://openalex.org/C108094655","wikidata":"https://www.wikidata.org/wiki/Q181593","display_name":"Sorting algorithm","level":3,"score":0.27799999713897705},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.27059999108314514},{"id":"https://openalex.org/C145685049","wikidata":"https://www.wikidata.org/wiki/Q4454941","display_name":"Euclidean minimum spanning tree","level":4,"score":0.26989999413490295},{"id":"https://openalex.org/C96563100","wikidata":"https://www.wikidata.org/wiki/Q8037118","display_name":"Worst-case complexity","level":3,"score":0.26179999113082886},{"id":"https://openalex.org/C64731005","wikidata":"https://www.wikidata.org/wiki/Q333464","display_name":"Analysis of algorithms","level":2,"score":0.25440001487731934},{"id":"https://openalex.org/C53051483","wikidata":"https://www.wikidata.org/wiki/Q861555","display_name":"Cube (algebra)","level":2,"score":0.2531000077724457}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:drops-oai.dagstuhl.de:26038","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.2","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol370-swat2026/LIPIcs.SWAT.2026.2/LIPIcs.SWAT.2026.2.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"publishedVersion"},{"id":"doi:10.4230/lipics.swat.2026.2","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.swat.2026.2","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":""}],"best_oa_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:26038","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.2","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol370-swat2026/LIPIcs.SWAT.2026.2/LIPIcs.SWAT.2026.2.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7163894009.pdf","grobid_xml":"https://content.openalex.org/works/W7163894009.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Surprisingly,":[0],"the":[1,5,21,25,42,91,108,118,147],"question":[2],"of":[3,8,24,44,73,123],"bounding":[4],"maximum":[6],"number":[7],"operations":[9],"undergone":[10],"by":[11,59,65],"each":[12],"individual":[13],"element":[14],"in":[15,76,86,121],"an":[16,132],"algorithm":[17,26,135],"-":[18,27],"known":[19,149],"as":[20,51,89],"fragile":[22,74],"complexity":[23,75],"has":[28],"not":[29],"received":[30],"much":[31],"attention.":[32],"In":[33],"a":[34,60,71,138],"foundational":[35],"paper,":[36],"Afshani":[37,66],"et":[38,67],"al.":[39],"(2019)":[40],"developed":[41],"concept":[43],"fragility":[45],"and":[46,53,98,112,126,140],"explored":[47],"classic":[48],"problems":[49,114],"such":[50,88],"sorting":[52],"selection":[54],"from":[55],"this":[56],"perspective.":[57],"Motivated":[58],"suggestion":[61],"for":[62,107],"future":[63],"research":[64],"al.,":[68],"we":[69],"initiate":[70],"study":[72],"computational":[77],"geometry.":[78],"We":[79,130],"obtain":[80],"bounds":[81],"on":[82],"several":[83],"time-honored":[84],"questions":[85],"2D":[87],"computing":[90],"maxima,":[92,109],"closest":[93],"pair,":[94],"convex":[95,110],"hull,":[96,111],"triangulation,":[97],"approximate":[99],"Euclidean":[100],"Minimum":[101],"Spanning":[102],"Tree":[103],"(apx-EMST).":[104],"Our":[105],"algorithms":[106,120],"triangulation":[113],"are":[115],"competitive":[116],"with":[117],"classical":[119],"terms":[122],"worst-case":[124],"runtime":[125],"guarantee":[127],"polylogarithmic":[128,153],"fragility.":[129],"present":[131],"O(nlog\u00b2n)":[133],"time":[134],"that":[136],"returns":[137],"1.0125-apx-EMST":[139],"achieves":[141],"O(log\u00b2":[142],"n)":[143],"fragility,":[144],"thus":[145],"matching":[146],"best":[148],"performance":[150],"up":[151],"to":[152],"factors.":[154]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-06-09T00:00:00"}