{"id":"https://openalex.org/W2109075404","doi":"https://doi.org/10.1017/s1471068404002261","title":"Computing convex hulls with a linear solver","display_name":"Computing convex hulls with a linear solver","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2109075404","doi":"https://doi.org/10.1017/s1471068404002261","mag":"2109075404"},"language":"en","primary_location":{"id":"doi:10.1017/s1471068404002261","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s1471068404002261","pdf_url":null,"source":{"id":"https://openalex.org/S59670734","display_name":"Theory and Practice of Logic Programming","issn_l":"1471-0684","issn":["1471-0684","1475-3081"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory and Practice of Logic Programming","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/A5069559562","display_name":"Florence Benoy","orcid":null},"institutions":[{"id":"https://openalex.org/I20581793","display_name":"University of Kent","ror":"https://ror.org/00xkeyj56","country_code":"GB","type":"education","lineage":["https://openalex.org/I20581793"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"FLORENCE BENOY","raw_affiliation_strings":["Computing Laboratory, University of Kent, Canterbury, Kent, UK (e-mail:","Computing Laboratory, University of Kent, Canterbury, Kent, UK (e-mail: p.m.benoy@kent.ac.uk, a.m.king@kent.ac.uk#TAB#"],"affiliations":[{"raw_affiliation_string":"Computing Laboratory, University of Kent, Canterbury, Kent, UK (e-mail:","institution_ids":["https://openalex.org/I20581793"]},{"raw_affiliation_string":"Computing Laboratory, University of Kent, Canterbury, Kent, UK (e-mail: p.m.benoy@kent.ac.uk, a.m.king@kent.ac.uk#TAB#","institution_ids":["https://openalex.org/I20581793"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103107567","display_name":"Andy King","orcid":"https://orcid.org/0000-0001-5806-4822"},"institutions":[{"id":"https://openalex.org/I20581793","display_name":"University of Kent","ror":"https://ror.org/00xkeyj56","country_code":"GB","type":"education","lineage":["https://openalex.org/I20581793"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"ANDY KING","raw_affiliation_strings":["Computing Laboratory, University of Kent, Canterbury, Kent, UK (e-mail:","Computing Laboratory, University of Kent, Canterbury, Kent, UK (e-mail: p.m.benoy@kent.ac.uk, a.m.king@kent.ac.uk#TAB#"],"affiliations":[{"raw_affiliation_string":"Computing Laboratory, University of Kent, Canterbury, Kent, UK (e-mail:","institution_ids":["https://openalex.org/I20581793"]},{"raw_affiliation_string":"Computing Laboratory, University of Kent, Canterbury, Kent, UK (e-mail: p.m.benoy@kent.ac.uk, a.m.king@kent.ac.uk#TAB#","institution_ids":["https://openalex.org/I20581793"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5106430092","display_name":"Fred Mesnard","orcid":null},"institutions":[{"id":"https://openalex.org/I24715933","display_name":"University of Reunion Island","ror":"https://ror.org/005ypkf75","country_code":"RE","type":"education","lineage":["https://openalex.org/I24715933"]}],"countries":["RE"],"is_corresponding":false,"raw_author_name":"FRED MESNARD","raw_affiliation_strings":["Iremia, Universit\u00e9 de La R\u00e9union, France (e-mail:","Iremia, Universit\u00e9 de La R\u00e9union, France (e-mail: fred@univ-reunion.fr)"],"affiliations":[{"raw_affiliation_string":"Iremia, Universit\u00e9 de La R\u00e9union, France (e-mail:","institution_ids":["https://openalex.org/I24715933"]},{"raw_affiliation_string":"Iremia, Universit\u00e9 de La R\u00e9union, France (e-mail: fred@univ-reunion.fr)","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5069559562"],"corresponding_institution_ids":["https://openalex.org/I20581793"],"apc_list":null,"apc_paid":null,"fwci":2.1081,"has_fulltext":false,"cited_by_count":33,"citation_normalized_percentile":{"value":0.86993175,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"5","issue":"1-2","first_page":"259","last_page":"271"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9998999834060669,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10743","display_name":"Software Testing and Debugging Techniques","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/1712","display_name":"Software"},"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/convex-hull","display_name":"Convex hull","score":0.8392754793167114},{"id":"https://openalex.org/keywords/polyhedron","display_name":"Polyhedron","score":0.811255931854248},{"id":"https://openalex.org/keywords/prolog","display_name":"Prolog","score":0.7483330965042114},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7029575705528259},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.6132926344871521},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.5831268429756165},{"id":"https://openalex.org/keywords/convex-polytope","display_name":"Convex polytope","score":0.5631611943244934},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.544154942035675},{"id":"https://openalex.org/keywords/constraint-logic-programming","display_name":"Constraint logic programming","score":0.5134338140487671},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.49726369976997375},{"id":"https://openalex.org/keywords/hull","display_name":"Hull","score":0.48800602555274963},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.4450390934944153},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.4277363419532776},{"id":"https://openalex.org/keywords/constraint-programming","display_name":"Constraint programming","score":0.4108070731163025},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4015966057777405},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.3614446520805359},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3532941937446594},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3154183626174927},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.30576983094215393},{"id":"https://openalex.org/keywords/constraint-satisfaction","display_name":"Constraint satisfaction","score":0.28345006704330444},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.20922094583511353},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.15337347984313965},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12875217199325562},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07686313986778259}],"concepts":[{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.8392754793167114},{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.811255931854248},{"id":"https://openalex.org/C81721847","wikidata":"https://www.wikidata.org/wiki/Q163468","display_name":"Prolog","level":2,"score":0.7483330965042114},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7029575705528259},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.6132926344871521},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.5831268429756165},{"id":"https://openalex.org/C110943637","wikidata":"https://www.wikidata.org/wiki/Q4129097","display_name":"Convex polytope","level":5,"score":0.5631611943244934},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.544154942035675},{"id":"https://openalex.org/C176783269","wikidata":"https://www.wikidata.org/wiki/Q5164378","display_name":"Constraint logic programming","level":4,"score":0.5134338140487671},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.49726369976997375},{"id":"https://openalex.org/C37423430","wikidata":"https://www.wikidata.org/wiki/Q6750281","display_name":"Hull","level":2,"score":0.48800602555274963},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.4450390934944153},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.4277363419532776},{"id":"https://openalex.org/C173404611","wikidata":"https://www.wikidata.org/wiki/Q528588","display_name":"Constraint programming","level":3,"score":0.4108070731163025},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4015966057777405},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.3614446520805359},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3532941937446594},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3154183626174927},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.30576983094215393},{"id":"https://openalex.org/C44616089","wikidata":"https://www.wikidata.org/wiki/Q30158686","display_name":"Constraint satisfaction","level":3,"score":0.28345006704330444},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.20922094583511353},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.15337347984313965},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12875217199325562},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07686313986778259},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.0},{"id":"https://openalex.org/C199104240","wikidata":"https://www.wikidata.org/wiki/Q118291","display_name":"Marine engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C137631369","wikidata":"https://www.wikidata.org/wiki/Q7617831","display_name":"Stochastic programming","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1017/s1471068404002261","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s1471068404002261","pdf_url":null,"source":{"id":"https://openalex.org/S59670734","display_name":"Theory and Practice of Logic Programming","issn_l":"1471-0684","issn":["1471-0684","1475-3081"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory and Practice of Logic Programming","raw_type":"journal-article"},{"id":"pmh:oai:kar.kent.ac.uk:37639","is_oa":false,"landing_page_url":"https://doi.org/10.1017/S1471068404002261>)","pdf_url":null,"source":{"id":"https://openalex.org/S4377196264","display_name":"Kent Academic Repository (University of Kent)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I20581793","host_organization_name":"University of Kent","host_organization_lineage":["https://openalex.org/I20581793"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W8956175","https://openalex.org/W1479857163","https://openalex.org/W1481517572","https://openalex.org/W1487657751","https://openalex.org/W1488214424","https://openalex.org/W1496121453","https://openalex.org/W1507967078","https://openalex.org/W1512982031","https://openalex.org/W1524883003","https://openalex.org/W1558952152","https://openalex.org/W1575672296","https://openalex.org/W1996679397","https://openalex.org/W2132661148","https://openalex.org/W2151697249","https://openalex.org/W2171834275","https://openalex.org/W2272316422","https://openalex.org/W2491413729"],"related_works":["https://openalex.org/W1486916474","https://openalex.org/W1531664660","https://openalex.org/W1597500234","https://openalex.org/W1567852657","https://openalex.org/W2097415053","https://openalex.org/W1596719193","https://openalex.org/W2365168741","https://openalex.org/W1591583250","https://openalex.org/W2525470665","https://openalex.org/W1591778271"],"abstract_inverted_index":{"A":[0],"programming":[1],"tactic":[2],"involving":[3],"polyhedra":[4],"is":[5,43],"reported":[6],"that":[7,28,42],"has":[8],"been":[9],"widely":[10],"applied":[11],"in":[12,45],"the":[13,23],"polyhedral":[14,32],"analysis":[15,33],"of":[16,25],"(constraint)":[17],"logic":[18],"programs.":[19],"The":[20],"method":[21],"enables":[22],"computations":[24],"convex":[26],"hulls":[27],"are":[29],"required":[30],"for":[31],"to":[34],"be":[35],"coded":[36],"with":[37],"linear":[38],"constraint":[39],"solving":[40],"machinery":[41],"available":[44],"many":[46],"Prolog":[47],"systems.":[48]},"counts_by_year":[{"year":2023,"cited_by_count":6},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}