{"id":"https://openalex.org/W2067705970","doi":"https://doi.org/10.1137/0213054","title":"Cylindrical Algebraic Decomposition I: The Basic Algorithm","display_name":"Cylindrical Algebraic Decomposition I: The Basic Algorithm","publication_year":1984,"publication_date":"1984-11-01","ids":{"openalex":"https://openalex.org/W2067705970","doi":"https://doi.org/10.1137/0213054","mag":"2067705970"},"language":"en","primary_location":{"id":"doi:10.1137/0213054","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0213054","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","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/A5055056438","display_name":"Dennis S. Arnon","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Dennis S. Arnon","raw_affiliation_strings":["Xerox-PARC, Palo Alto, CA"],"affiliations":[{"raw_affiliation_string":"Xerox-PARC, Palo Alto, CA","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109076166","display_name":"George E. Collins","orcid":null},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"George E. Collins","raw_affiliation_strings":["University of Wisconsin\u2014Madison, Madison,"],"affiliations":[{"raw_affiliation_string":"University of Wisconsin\u2014Madison, Madison,","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061480464","display_name":"Scott McCallum","orcid":"https://orcid.org/0000-0002-5682-7993"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Scott McCallum","raw_affiliation_strings":["University of Toronto, Toronto, Ont., Canada,"],"affiliations":[{"raw_affiliation_string":"University of Toronto, Toronto, Ont., Canada,","institution_ids":["https://openalex.org/I185261750"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5055056438"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.0548,"has_fulltext":false,"cited_by_count":356,"citation_normalized_percentile":{"value":0.95505618,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"13","issue":"4","first_page":"865","last_page":"877"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9986000061035156,"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":0.9986000061035156,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9983999729156494,"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/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9962000250816345,"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/cad","display_name":"CAD","score":0.6501247882843018},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.648700475692749},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5621370673179626},{"id":"https://openalex.org/keywords/adjacency-list","display_name":"Adjacency list","score":0.5136608481407166},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.49487966299057007},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.4803272783756256},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4758686423301697},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.4600844383239746},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.4577019214630127},{"id":"https://openalex.org/keywords/quantifier-elimination","display_name":"Quantifier elimination","score":0.41522717475891113},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3822878301143646},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.29456621408462524},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.27494528889656067},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10883629322052002}],"concepts":[{"id":"https://openalex.org/C194789388","wikidata":"https://www.wikidata.org/wiki/Q17855283","display_name":"CAD","level":2,"score":0.6501247882843018},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.648700475692749},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5621370673179626},{"id":"https://openalex.org/C110484373","wikidata":"https://www.wikidata.org/wiki/Q264398","display_name":"Adjacency list","level":2,"score":0.5136608481407166},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.49487966299057007},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.4803272783756256},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4758686423301697},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.4600844383239746},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.4577019214630127},{"id":"https://openalex.org/C32278780","wikidata":"https://www.wikidata.org/wiki/Q1849020","display_name":"Quantifier elimination","level":2,"score":0.41522717475891113},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3822878301143646},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.29456621408462524},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.27494528889656067},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10883629322052002},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C199639397","wikidata":"https://www.wikidata.org/wiki/Q1788588","display_name":"Engineering drawing","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/0213054","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0213054","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},{"id":"pmh:oai:docs.lib.purdue.edu:cstech-1350","is_oa":false,"landing_page_url":"https://docs.lib.purdue.edu/cstech/351","pdf_url":null,"source":{"id":"https://openalex.org/S4377196310","display_name":"Purdue e-Pubs (Purdue University System)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801333002","host_organization_name":"Purdue University System","host_organization_lineage":["https://openalex.org/I2801333002"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Department of Computer Science Technical Reports","raw_type":"text"},{"id":"pmh:oai:docs.lib.purdue.edu:cstech-1351","is_oa":false,"landing_page_url":"https://docs.lib.purdue.edu/cstech/352","pdf_url":null,"source":{"id":"https://openalex.org/S4377196310","display_name":"Purdue e-Pubs (Purdue University System)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801333002","host_organization_name":"Purdue University System","host_organization_lineage":["https://openalex.org/I2801333002"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Department of Computer Science Technical Reports","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.5600000023841858}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1513644114","https://openalex.org/W1527913126","https://openalex.org/W1598625331","https://openalex.org/W1815267262","https://openalex.org/W1988416919","https://openalex.org/W1988503310","https://openalex.org/W1999927144","https://openalex.org/W2008957088","https://openalex.org/W2016390696","https://openalex.org/W2033013465","https://openalex.org/W2131258401","https://openalex.org/W2316129477","https://openalex.org/W3190671301","https://openalex.org/W4229917934","https://openalex.org/W4231471038","https://openalex.org/W4237013870","https://openalex.org/W4240096288","https://openalex.org/W4389011534"],"related_works":["https://openalex.org/W1632876905","https://openalex.org/W2167856990","https://openalex.org/W2738238629","https://openalex.org/W2087001307","https://openalex.org/W4300611326","https://openalex.org/W2217564470","https://openalex.org/W2337746918","https://openalex.org/W1663884662","https://openalex.org/W2047879298","https://openalex.org/W4301445453"],"abstract_inverted_index":{"Given":[0],"a":[1,7,33,37,46,93,120],"set":[2],"of":[3,12,27,45,87,95,113],"r-variate":[4],"integral":[5],"polynomials,":[6],"cylindrical":[8],"algebraic":[9],"decomposition":[10],"(cad)":[11],"euclidean":[13],"r-space":[14,115],"$E^r":[15,18],"$":[16,19],"partitions":[17],"into":[20],"connected":[21],"subsets":[22],"compatible":[23],"with":[24],"the":[25,28,75,85,110,114,123],"zeros":[26],"polynomials.":[29],"Each":[30],"subset":[31],"is":[32,100],"cell":[34],"Collins":[35],"gave":[36],"cad":[38,55,94,116],"construction":[39],"algorithm":[40,56,82,125],"in":[41,103,126],"1975,":[42],"as":[43,90],"part":[44],"quantifier":[47],"elimination":[48],"procedure":[49],"for":[50,122],"real":[51],"closed":[52],"fields.":[53],"The":[54],"has":[57],"found":[58],"diverse":[59],"applications":[60,65],"(optimization,":[61],"curve":[62],"display);":[63],"new":[64],"have":[66],"been":[67],"proposed":[68],"(term":[69],"rewriting":[70],"systems,":[71],"motion":[72],"planning).":[73],"In":[74,105],"present":[76],"two-part":[77],"paper,":[78],"we":[79,108],"give":[80],"an":[81],"which":[83],"determines":[84],"pairs":[86],"adjacent":[88],"cells":[89],"it":[91],"constructs":[92],"$E^2":[96],"$.":[97],"Such":[98],"information":[99],"often":[101],"useful":[102],"applications.":[104],"Part":[106,127],"I":[107],"describe":[109],"essential":[111],"features":[112],"algorithm,":[117],"to":[118],"provide":[119],"framework":[121],"adjacency":[124],"II.":[128]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":12},{"year":2015,"cited_by_count":16},{"year":2014,"cited_by_count":16},{"year":2013,"cited_by_count":13},{"year":2012,"cited_by_count":10}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}