{"id":"https://openalex.org/W2051595244","doi":"https://doi.org/10.1145/1005285.1005303","title":"Efficient projection orders for CAD","display_name":"Efficient projection orders for CAD","publication_year":2004,"publication_date":"2004-07-04","ids":{"openalex":"https://openalex.org/W2051595244","doi":"https://doi.org/10.1145/1005285.1005303","mag":"2051595244"},"language":"en","primary_location":{"id":"doi:10.1145/1005285.1005303","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1005285.1005303","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2004 international symposium on Symbolic and algebraic computation","raw_type":"proceedings-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/A5086267365","display_name":"Andreas Dolzmann","orcid":null},"institutions":[{"id":"https://openalex.org/I186354981","display_name":"University of Passau","ror":"https://ror.org/05ydjnb78","country_code":"DE","type":"education","lineage":["https://openalex.org/I186354981"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Andreas Dolzmann","raw_affiliation_strings":["Universit\u00e4t Passau, Germany","Universitat Passau, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e4t Passau, Germany","institution_ids":["https://openalex.org/I186354981"]},{"raw_affiliation_string":"Universitat Passau, Germany","institution_ids":["https://openalex.org/I186354981"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065334266","display_name":"Andreas Seidl","orcid":null},"institutions":[{"id":"https://openalex.org/I13134134","display_name":"Universidad de Cantabria","ror":"https://ror.org/046ffzj20","country_code":"ES","type":"education","lineage":["https://openalex.org/I13134134"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Andreas Seidl","raw_affiliation_strings":["Universidad de Cantabria, Spain","Universidad de Cantabria (Spain)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universidad de Cantabria, Spain","institution_ids":["https://openalex.org/I13134134"]},{"raw_affiliation_string":"Universidad de Cantabria (Spain)","institution_ids":["https://openalex.org/I13134134"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039342399","display_name":"Thomas Sturm","orcid":"https://orcid.org/0000-0002-8088-340X"},"institutions":[{"id":"https://openalex.org/I186354981","display_name":"University of Passau","ror":"https://ror.org/05ydjnb78","country_code":"DE","type":"education","lineage":["https://openalex.org/I186354981"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Thomas Sturm","raw_affiliation_strings":["Universit\u00e4t Passau, Germany","Universitat Passau, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e4t Passau, Germany","institution_ids":["https://openalex.org/I186354981"]},{"raw_affiliation_string":"Universitat Passau, Germany","institution_ids":["https://openalex.org/I186354981"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.5623,"has_fulltext":false,"cited_by_count":100,"citation_normalized_percentile":{"value":0.91975785,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"111","last_page":"118"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9991999864578247,"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"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.998199999332428,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.996999979019165,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.7704858779907227},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.7463650703430176},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6397002339363098},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.569178581237793},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5504676699638367},{"id":"https://openalex.org/keywords/cad","display_name":"CAD","score":0.5423934459686279},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.541696310043335},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.49569594860076904},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.27766484022140503}],"concepts":[{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.7704858779907227},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.7463650703430176},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6397002339363098},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.569178581237793},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5504676699638367},{"id":"https://openalex.org/C194789388","wikidata":"https://www.wikidata.org/wiki/Q17855283","display_name":"CAD","level":2,"score":0.5423934459686279},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.541696310043335},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.49569594860076904},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.27766484022140503},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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":5,"locations":[{"id":"doi:10.1145/1005285.1005303","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1005285.1005303","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2004 international symposium on Symbolic and algebraic computation","raw_type":"proceedings-article"},{"id":"pmh:hdl:10068/152147","is_oa":false,"landing_page_url":"http://hdl.handle.net/10068/152147","pdf_url":null,"source":{"id":"https://openalex.org/S4377196900","display_name":"OpenGrey (Institut de l'Information Scientifique et Technique)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1295345811","host_organization_name":"Institut de l'Information Scientifique et Technique","host_organization_lineage":["https://openalex.org/I1295345811"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"R - Report"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.3.5359","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.5359","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.fmi.uni-passau.de/forschung/mip-berichte/MIP-0401.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.89.767","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.89.767","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://staff.fim.uni-passau.de/~sturm/publications/p111-dolzmann.pdf","raw_type":"text"},{"id":"pmh:oai:aleph.bib-bvb.de:BVB01-010699149","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W39238065","https://openalex.org/W1491532135","https://openalex.org/W1558198085","https://openalex.org/W1565449944","https://openalex.org/W1965768600","https://openalex.org/W1986264093","https://openalex.org/W2007074311","https://openalex.org/W2021431116","https://openalex.org/W2022125816","https://openalex.org/W2031948211","https://openalex.org/W2033013465","https://openalex.org/W2040139795","https://openalex.org/W2052869011","https://openalex.org/W2054581185","https://openalex.org/W2067705970","https://openalex.org/W2077320196","https://openalex.org/W4229917934","https://openalex.org/W4234426551"],"related_works":["https://openalex.org/W2320366403","https://openalex.org/W3204197061","https://openalex.org/W4251350712","https://openalex.org/W637098845","https://openalex.org/W2410116073","https://openalex.org/W3044972437","https://openalex.org/W2275866607","https://openalex.org/W3198805702","https://openalex.org/W2951540481","https://openalex.org/W2506951661"],"abstract_inverted_index":{"We":[0],"introduce":[1],"an":[2],"efficient":[3],"algorithm":[4,17,61],"for":[5,11],"determining":[6],"a":[7,21],"suitable":[8],"projection":[9,37],"order":[10],"performing":[12],"cylindrical":[13],"algebraic":[14],"decomposition.":[15],"Our":[16],"is":[18],"motivated":[19],"by":[20,59],"statistical":[22,51],"analysis":[23,30],"of":[24],"comprehensive":[25],"test":[26],"set":[27],"computations.":[28],"This":[29],"introduces":[31],"several":[32],"measures":[33],"on":[34],"both":[35],"the":[36,40,56],"sets":[38],"and":[39],"entire":[41],"computation,":[42],"which":[43],"turn":[44],"out":[45],"to":[46,65],"be":[47],"highly":[48],"correlated.":[49],"The":[50],"data":[52],"also":[53],"shows":[54],"that":[55],"orders":[57],"generated":[58],"our":[60],"are":[62],"significantly":[63],"close":[64],"optimal.":[66]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":14},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":4}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}
