{"id":"https://openalex.org/W2640923064","doi":"https://doi.org/10.1145/3275242","title":"Computing the Homology of Basic Semialgebraic Sets in Weak Exponential Time","display_name":"Computing the Homology of Basic Semialgebraic Sets in Weak Exponential Time","publication_year":2018,"publication_date":"2018-12-16","ids":{"openalex":"https://openalex.org/W2640923064","doi":"https://doi.org/10.1145/3275242","mag":"2640923064"},"language":"en","primary_location":{"id":"doi:10.1145/3275242","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3275242","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1706.07473","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Peter B\u00fcrgisser","orcid":null},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Peter B\u00fcrgisser","raw_affiliation_strings":["Technische Universit\u00e4t Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technische Universit\u00e4t Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Felipe Cucker","orcid":null},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Felipe Cucker","raw_affiliation_strings":["City University of Hong Kong, Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"City University of Hong Kong, Hong Kong","institution_ids":["https://openalex.org/I168719708"]}]},{"author_position":"last","author":{"id":null,"display_name":"Pierre Lairez","orcid":null},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Pierre Lairez","raw_affiliation_strings":["Inria, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Inria, France","institution_ids":["https://openalex.org/I1326498283"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.5015,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.83713514,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"66","issue":"1","first_page":"1","last_page":"30"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.44119998812675476,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.44119998812675476,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.4309000074863434,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.045099999755620956,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.6948999762535095},{"id":"https://openalex.org/keywords/exponential-growth","display_name":"Exponential growth","score":0.667900025844574},{"id":"https://openalex.org/keywords/homology","display_name":"Homology (biology)","score":0.6312999725341797},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.40689998865127563},{"id":"https://openalex.org/keywords/torsion","display_name":"Torsion (gastropod)","score":0.39660000801086426},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.3343000113964081},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.32910001277923584}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7195000052452087},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.6948999762535095},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.667900025844574},{"id":"https://openalex.org/C165525559","wikidata":"https://www.wikidata.org/wiki/Q224180","display_name":"Homology (biology)","level":3,"score":0.6312999725341797},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5005999803543091},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.40689998865127563},{"id":"https://openalex.org/C77461463","wikidata":"https://www.wikidata.org/wiki/Q7827201","display_name":"Torsion (gastropod)","level":2,"score":0.39660000801086426},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3822000026702881},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.335999995470047},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3343000113964081},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.32910001277923584},{"id":"https://openalex.org/C3018263672","wikidata":"https://www.wikidata.org/wiki/Q1296251","display_name":"Efficient algorithm","level":2,"score":0.32749998569488525},{"id":"https://openalex.org/C85384003","wikidata":"https://www.wikidata.org/wiki/Q5421525","display_name":"Exponential polynomial","level":3,"score":0.32260000705718994},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.3111000061035156},{"id":"https://openalex.org/C71017364","wikidata":"https://www.wikidata.org/wiki/Q5421532","display_name":"Exponential time hypothesis","level":3,"score":0.2644999921321869},{"id":"https://openalex.org/C55974624","wikidata":"https://www.wikidata.org/wiki/Q1188504","display_name":"Exponential family","level":2,"score":0.26080000400543213},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.2567000091075897}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/3275242","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3275242","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1706.07473","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1706.07473","pdf_url":"https://arxiv.org/pdf/1706.07473","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-01545657v2","is_oa":true,"landing_page_url":"https://hal.science/hal-01545657","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of the ACM (JACM), 2018, 66 (1), pp.1-30. ⟨10.1145/3275242⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1706.07473","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1706.07473","pdf_url":"https://arxiv.org/pdf/1706.07473","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W1561337879","https://openalex.org/W1589087843","https://openalex.org/W1965654736","https://openalex.org/W1970798152","https://openalex.org/W1971666500","https://openalex.org/W1991813962","https://openalex.org/W2006459820","https://openalex.org/W2018089423","https://openalex.org/W2031859062","https://openalex.org/W2033943710","https://openalex.org/W2043907498","https://openalex.org/W2051610907","https://openalex.org/W2063917062","https://openalex.org/W2065367476","https://openalex.org/W2067607283","https://openalex.org/W2071846104","https://openalex.org/W2076067331","https://openalex.org/W2078290150","https://openalex.org/W2079400692","https://openalex.org/W2082387287","https://openalex.org/W2086785654","https://openalex.org/W2088141885","https://openalex.org/W2090930073","https://openalex.org/W2092920739","https://openalex.org/W2118254039","https://openalex.org/W2129635337","https://openalex.org/W2134709850","https://openalex.org/W2141062816","https://openalex.org/W2151549243","https://openalex.org/W2160725437","https://openalex.org/W2162826883","https://openalex.org/W2163243521","https://openalex.org/W2279788372","https://openalex.org/W2316564661","https://openalex.org/W2322909536","https://openalex.org/W2592503220","https://openalex.org/W2962955948","https://openalex.org/W2964330200","https://openalex.org/W4213171111","https://openalex.org/W4254852607","https://openalex.org/W6644664788","https://openalex.org/W6672845998"],"related_works":["https://openalex.org/W3117168532","https://openalex.org/W2582431911","https://openalex.org/W1875534739","https://openalex.org/W1619643520","https://openalex.org/W4293369515","https://openalex.org/W1986237181","https://openalex.org/W4225499446","https://openalex.org/W1688230337","https://openalex.org/W2922936069","https://openalex.org/W3123452453"],"abstract_inverted_index":{"We":[0],"describe":[1],"and":[2,12],"analyze":[3],"an":[4],"algorithm":[5,43],"for":[6,56,70],"computing":[7],"the":[8,35,39,42,47,50],"homology":[9],"(Betti":[10],"numbers":[11],"torsion":[13],"coefficients)":[14],"of":[15,27,30,37,41,49],"basic":[16],"semialgebraic":[17],"sets":[18],"that":[19,62],"works":[20],"in":[21,34,46],"weak":[22],"exponential":[23,45,65],"time.":[24],"That":[25],"is,":[26],"a":[28,60],"set":[29],"exponentially":[31],"small":[32],"measure":[33],"space":[36],"data,":[38],"cost":[40],"is":[44,63,68],"size":[48],"data.":[51],"All":[52],"algorithms":[53],"previously":[54],"proposed":[55],"this":[57,67],"problem":[58],"have":[59],"complexity":[61],"doubly":[64],"(and":[66],"so":[69],"almost":[71],"all":[72],"data).":[73]},"counts_by_year":[{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":4}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2017-06-30T00:00:00"}