{"id":"https://openalex.org/W2019890869","doi":"https://doi.org/10.1007/s00453-007-9010-0","title":"A Tight Lower Bound for Computing the Diameter of a 3D Convex Polytope","display_name":"A Tight Lower Bound for Computing the Diameter of a 3D Convex Polytope","publication_year":2007,"publication_date":"2007-09-21","ids":{"openalex":"https://openalex.org/W2019890869","doi":"https://doi.org/10.1007/s00453-007-9010-0","mag":"2019890869"},"language":"en","primary_location":{"id":"doi:10.1007/s00453-007-9010-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00453-007-9010-0","pdf_url":null,"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":null,"license_id":null,"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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004130370","display_name":"Herv\u00e9 Fournier","orcid":null},"institutions":[{"id":"https://openalex.org/I195731000","display_name":"Universit\u00e9 de Versailles Saint-Quentin-en-Yvelines","ror":"https://ror.org/03mkjjy25","country_code":"FR","type":"education","lineage":["https://openalex.org/I195731000","https://openalex.org/I277688954"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Herv\u00e9 Fournier","raw_affiliation_strings":["Laboratoire PRiSM, Universit\u00e9 de Versailles Saint-Quentin-en-Yvelines, 45 avenue des \u00c9tats-Unis, 78035, Versailles cedex, France","Universit\u00e9 de Versailles Saint-Quentin-en-Yvelines, Laboratoire PRISM, 45, Avenue des Etats-Unis, 78035 Versailles cedex, France#TAB#"],"affiliations":[{"raw_affiliation_string":"Laboratoire PRiSM, Universit\u00e9 de Versailles Saint-Quentin-en-Yvelines, 45 avenue des \u00c9tats-Unis, 78035, Versailles cedex, France","institution_ids":["https://openalex.org/I195731000"]},{"raw_affiliation_string":"Universit\u00e9 de Versailles Saint-Quentin-en-Yvelines, Laboratoire PRISM, 45, Avenue des Etats-Unis, 78035 Versailles cedex, France#TAB#","institution_ids":["https://openalex.org/I195731000"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019937157","display_name":"Antoine Vigneron","orcid":"https://orcid.org/0000-0003-3586-3431"},"institutions":[{"id":"https://openalex.org/I4210159481","display_name":"Math\u00e9matiques et Informatique Appliqu\u00e9es du G\u00e9nome \u00e0 l'Environnement","ror":"https://ror.org/05qdnns64","country_code":"FR","type":"facility","lineage":["https://openalex.org/I4210088668","https://openalex.org/I4210099460","https://openalex.org/I4210159481"]},{"id":"https://openalex.org/I4387153087","display_name":"Math\u00e9matiques et Informatique Appliqu\u00e9es","ror":"https://ror.org/00780az30","country_code":null,"type":"facility","lineage":["https://openalex.org/I22248866","https://openalex.org/I277688954","https://openalex.org/I277688954","https://openalex.org/I4210088668","https://openalex.org/I4387153087"]},{"id":"https://openalex.org/I1314251682","display_name":"Institut National de la Recherche Agronomique","ror":"https://ror.org/05y503v71","country_code":"MA","type":"facility","lineage":["https://openalex.org/I1314251682"]}],"countries":["FR","MA"],"is_corresponding":false,"raw_author_name":"Antoine Vigneron","raw_affiliation_strings":["INRA, UR341 Math\u00e9matiques et Informatique Appliqu\u00e9es, Domaine de Vilvert, 78352, Jouy-en-Josas cedex, France","UR341 Math\u00e9matiques et Informatique Appliqu\u00e9es, INRA, Domaine de Vilvert, 78352, Jouy-en-Josas cedex, France#TAB#"],"affiliations":[{"raw_affiliation_string":"INRA, UR341 Math\u00e9matiques et Informatique Appliqu\u00e9es, Domaine de Vilvert, 78352, Jouy-en-Josas cedex, France","institution_ids":["https://openalex.org/I4210159481"]},{"raw_affiliation_string":"UR341 Math\u00e9matiques et Informatique Appliqu\u00e9es, INRA, Domaine de Vilvert, 78352, Jouy-en-Josas cedex, France#TAB#","institution_ids":["https://openalex.org/I1314251682","https://openalex.org/I4387153087"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5004130370"],"corresponding_institution_ids":["https://openalex.org/I195731000"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":1.073,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.83036915,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"49","issue":"3","first_page":"245","last_page":"257"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":1.0,"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":1.0,"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":0.998199999332428,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/polytope","display_name":"Polytope","score":0.8256968259811401},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.808586835861206},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7545815110206604},{"id":"https://openalex.org/keywords/convex-polytope","display_name":"Convex polytope","score":0.7531054019927979},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.507419764995575},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5029696822166443},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.49730947613716125},{"id":"https://openalex.org/keywords/birkhoff-polytope","display_name":"Birkhoff polytope","score":0.4594377875328064},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.44449105858802795},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4270830750465393},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.3896143436431885},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36170047521591187},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.23699945211410522},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.20594936609268188},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.10804447531700134},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10449978709220886}],"concepts":[{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.8256968259811401},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.808586835861206},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7545815110206604},{"id":"https://openalex.org/C110943637","wikidata":"https://www.wikidata.org/wiki/Q4129097","display_name":"Convex polytope","level":5,"score":0.7531054019927979},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.507419764995575},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5029696822166443},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.49730947613716125},{"id":"https://openalex.org/C206304794","wikidata":"https://www.wikidata.org/wiki/Q4916482","display_name":"Birkhoff polytope","level":5,"score":0.4594377875328064},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.44449105858802795},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4270830750465393},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.3896143436431885},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36170047521591187},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23699945211410522},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.20594936609268188},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.10804447531700134},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10449978709220886},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00453-007-9010-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00453-007-9010-0","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.108.3039","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.108.3039","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.prism.uvsq.fr/~hefou/publis/diameter.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-02668338v1","is_oa":false,"landing_page_url":"https://hal.inrae.fr/hal-02668338","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithmica, 2007, 49 (3), pp.245-257. ⟨10.1007/s00453-007-9010-0⟩","raw_type":"Journal articles"},{"id":"pmh:oai:scholarworks.unist.ac.kr:201301/19657","is_oa":false,"landing_page_url":"https://scholarworks.unist.ac.kr/handle/201301/19657","pdf_url":null,"source":{"id":"https://openalex.org/S4306401118","display_name":"Scholarworks@UNIST (Ulsan National Institute of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I48566637","host_organization_name":"Ulsan National Institute of Science and Technology","host_organization_lineage":["https://openalex.org/I48566637"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"ARTICLE"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W108314478","https://openalex.org/W1561337879","https://openalex.org/W1968215127","https://openalex.org/W1972369894","https://openalex.org/W2005314985","https://openalex.org/W2027387410","https://openalex.org/W2032022602","https://openalex.org/W2037877878","https://openalex.org/W2050386932","https://openalex.org/W2053928251","https://openalex.org/W2058127000","https://openalex.org/W2058432138","https://openalex.org/W2059985428","https://openalex.org/W2098355410","https://openalex.org/W2149906774","https://openalex.org/W2171743190","https://openalex.org/W2911302472","https://openalex.org/W3138944346","https://openalex.org/W4242246215","https://openalex.org/W4254977685"],"related_works":["https://openalex.org/W2953076628","https://openalex.org/W2085110259","https://openalex.org/W2963837916","https://openalex.org/W2773485609","https://openalex.org/W1854884900","https://openalex.org/W2949863507","https://openalex.org/W3012067785","https://openalex.org/W2069107464","https://openalex.org/W4288417334","https://openalex.org/W4243575619"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}