{"id":"https://openalex.org/W2105946172","doi":"https://doi.org/10.1007/s00453-008-9174-2","title":"Largest and Smallest Convex Hulls for Imprecise Points","display_name":"Largest and Smallest Convex Hulls for Imprecise Points","publication_year":2008,"publication_date":"2008-03-03","ids":{"openalex":"https://openalex.org/W2105946172","doi":"https://doi.org/10.1007/s00453-008-9174-2","mag":"2105946172"},"language":"en","primary_location":{"id":"doi:10.1007/s00453-008-9174-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-008-9174-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-008-9174-2.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00453-008-9174-2.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112453554","display_name":"Maarten L\u00f6ffler","orcid":null},"institutions":[{"id":"https://openalex.org/I193662353","display_name":"Utrecht University","ror":"https://ror.org/04pp8hn57","country_code":"NL","type":"education","lineage":["https://openalex.org/I193662353"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Maarten L\u00f6ffler","raw_affiliation_strings":["Department of Information and Computing Sciences, Utrecht University, Utrecht, The Netherlands","Utrecht University Department of Information and Computing Sciences Utrecht The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Information and Computing Sciences, Utrecht University, Utrecht, The Netherlands","institution_ids":["https://openalex.org/I193662353"]},{"raw_affiliation_string":"Utrecht University Department of Information and Computing Sciences Utrecht The Netherlands","institution_ids":["https://openalex.org/I193662353"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053874521","display_name":"Marc van Kreveld","orcid":"https://orcid.org/0000-0001-8208-3468"},"institutions":[{"id":"https://openalex.org/I193662353","display_name":"Utrecht University","ror":"https://ror.org/04pp8hn57","country_code":"NL","type":"education","lineage":["https://openalex.org/I193662353"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Marc van Kreveld","raw_affiliation_strings":["Department of Information and Computing Sciences, Utrecht University, Utrecht, The Netherlands","Utrecht University Department of Information and Computing Sciences Utrecht The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Information and Computing Sciences, Utrecht University, Utrecht, The Netherlands","institution_ids":["https://openalex.org/I193662353"]},{"raw_affiliation_string":"Utrecht University Department of Information and Computing Sciences Utrecht The Netherlands","institution_ids":["https://openalex.org/I193662353"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5112453554"],"corresponding_institution_ids":["https://openalex.org/I193662353"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":22.3337,"has_fulltext":true,"cited_by_count":115,"citation_normalized_percentile":{"value":0.99381547,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"56","issue":"2","first_page":"235","last_page":"269"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9997000098228455,"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":0.9997000098228455,"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9995999932289124,"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"}},{"id":"https://openalex.org/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8272556066513062},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.8241937160491943},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.738589882850647},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6229267120361328},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.544522762298584},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5268251299858093},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5104993581771851},{"id":"https://openalex.org/keywords/convex-combination","display_name":"Convex combination","score":0.5055971145629883},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.49708107113838196},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.46493029594421387},{"id":"https://openalex.org/keywords/convex-polytope","display_name":"Convex polytope","score":0.4550020694732666},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.39720797538757324},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35673877596855164},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2508987784385681},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.2415732443332672},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14238914847373962},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1343000829219818}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8272556066513062},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.8241937160491943},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.738589882850647},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6229267120361328},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.544522762298584},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5268251299858093},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5104993581771851},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.5055971145629883},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.49708107113838196},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.46493029594421387},{"id":"https://openalex.org/C110943637","wikidata":"https://www.wikidata.org/wiki/Q4129097","display_name":"Convex polytope","level":5,"score":0.4550020694732666},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.39720797538757324},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35673877596855164},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2508987784385681},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.2415732443332672},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14238914847373962},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1343000829219818},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s00453-008-9174-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-008-9174-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-008-9174-2.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.144.4246","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.144.4246","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.loria.fr/~everett/McGill-ISA/Bellairs-2009/background/hulls-loffler-vanKreveld.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.77.7058","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.77.7058","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.uu.nl/research/techreps/repo/CS-2006/2006-019.pdf","raw_type":"text"},{"id":"pmh:oai:dspace.library.uu.nl:1874/30496","is_oa":true,"landing_page_url":"http://dspace.library.uu.nl:8080/handle/1874/30496","pdf_url":null,"source":{"id":"https://openalex.org/S4306401649","display_name":"Utrecht University Repository (Utrecht University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I193662353","host_organization_name":"Utrecht University","host_organization_lineage":["https://openalex.org/I193662353"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:uu:oai:dspace.library.uu.nl:1874/30496","is_oa":true,"landing_page_url":"https://dspace.library.uu.nl/handle/1874/30496","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithmica. Springer","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s00453-008-9174-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-008-9174-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-008-9174-2.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.4099999964237213,"display_name":"Sustainable cities and communities"}],"awards":[{"id":"https://openalex.org/G3119829495","display_name":null,"funder_award_id":"642.065.503","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2105946172.pdf","grobid_xml":"https://content.openalex.org/works/W2105946172.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W29331208","https://openalex.org/W41655223","https://openalex.org/W77772846","https://openalex.org/W174419558","https://openalex.org/W179323378","https://openalex.org/W1501243125","https://openalex.org/W1526223692","https://openalex.org/W1550030874","https://openalex.org/W1554187075","https://openalex.org/W1968165428","https://openalex.org/W1980080397","https://openalex.org/W1981114840","https://openalex.org/W1994058693","https://openalex.org/W2006234597","https://openalex.org/W2007553965","https://openalex.org/W2017723092","https://openalex.org/W2022754388","https://openalex.org/W2025736494","https://openalex.org/W2026291033","https://openalex.org/W2043127280","https://openalex.org/W2047747795","https://openalex.org/W2050284373","https://openalex.org/W2060380213","https://openalex.org/W2066577300","https://openalex.org/W2069683521","https://openalex.org/W2070789991","https://openalex.org/W2071857538","https://openalex.org/W2104800753","https://openalex.org/W2108250208","https://openalex.org/W2125334953","https://openalex.org/W2128270135","https://openalex.org/W2132339863","https://openalex.org/W2135508018","https://openalex.org/W2139230981","https://openalex.org/W2143022779","https://openalex.org/W2609774945","https://openalex.org/W4244080821","https://openalex.org/W4252017042","https://openalex.org/W4385289538"],"related_works":["https://openalex.org/W2300145982","https://openalex.org/W2363904277","https://openalex.org/W981962503","https://openalex.org/W2580512045","https://openalex.org/W868123585","https://openalex.org/W2375652826","https://openalex.org/W2365830408","https://openalex.org/W1569666406","https://openalex.org/W4296997005","https://openalex.org/W1758159897"],"abstract_inverted_index":{"Assume":[0],"that":[1],"a":[2,15,50,60],"set":[3],"of":[4,27,74],"imprecise":[5],"points":[6],"is":[7,12,59],"given,":[8],"where":[9,57],"each":[10],"point":[11,20],"specified":[13],"by":[14,37,40],"region":[16,47],"in":[17,78],"which":[18],"the":[19,25,29,45,55],"may":[21],"lie.":[22],"We":[23,66],"study":[24],"problem":[26],"computing":[28],"smallest":[30],"and":[31,39,87],"largest":[32],"possible":[33],"convex":[34],"hulls,":[35],"measured":[36],"length":[38],"area.":[41],"Generally":[42],"we":[43,53],"assume":[44],"imprecision":[46],"to":[48,84],"be":[49],"square,":[51],"but":[52],"discuss":[54],"case":[56],"it":[58],"segment":[61],"or":[62],"circle":[63],"as":[64],"well.":[65],"give":[67],"polynomial":[68],"time":[69,80],"algorithms":[70],"for":[71,90],"several":[72],"variants":[73],"this":[75],"problem,":[76],"ranging":[77],"running":[79],"from":[81],"O(nlog":[82],"n)":[83],"O(n":[85],"13),":[86],"prove":[88],"NP-hardness":[89],"some":[91],"other":[92],"variants.":[93]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":13},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":8}],"updated_date":"2026-06-23T13:55:30.953635","created_date":"2025-10-10T00:00:00"}
