{"id":"https://openalex.org/W2048401959","doi":"https://doi.org/10.1016/0004-3702(88)90061-6","title":"Verifiable implementations of geometric algorithms using finite precision arithmetic","display_name":"Verifiable implementations of geometric algorithms using finite precision arithmetic","publication_year":1988,"publication_date":"1988-12-01","ids":{"openalex":"https://openalex.org/W2048401959","doi":"https://doi.org/10.1016/0004-3702(88)90061-6","mag":"2048401959"},"language":"en","primary_location":{"id":"doi:10.1016/0004-3702(88)90061-6","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0004-3702(88)90061-6","pdf_url":null,"source":{"id":"https://openalex.org/S196139623","display_name":"Artificial Intelligence","issn_l":"0004-3702","issn":["0004-3702","1872-7921"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Artificial Intelligence","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/A5039907465","display_name":"Victor Milenkovic","orcid":"https://orcid.org/0000-0001-8524-9742"},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Victor J. Milenkovic","raw_affiliation_strings":["Department of Computer Science, Carnegie-Mellon University, Pittsburgh, PA 15213, U.S.A","Harvard University, Cambridge, Ma.#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Carnegie-Mellon University, Pittsburgh, PA 15213, U.S.A","institution_ids":[]},{"raw_affiliation_string":"Harvard University, Cambridge, Ma.#TAB#","institution_ids":["https://openalex.org/I136199984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5039907465"],"corresponding_institution_ids":["https://openalex.org/I136199984"],"apc_list":{"value":3670,"currency":"USD","value_usd":3670},"apc_paid":null,"fwci":16.57,"has_fulltext":false,"cited_by_count":153,"citation_normalized_percentile":{"value":0.99455984,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"37","issue":"1-3","first_page":"377","last_page":"401"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9991000294685364,"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":0.9991000294685364,"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/T11159","display_name":"Manufacturing Process and Optimization","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"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/T11583","display_name":"Advanced Measurement and Metrology Techniques","score":0.992900013923645,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"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/normalization","display_name":"Normalization (sociology)","score":0.7969383597373962},{"id":"https://openalex.org/keywords/verifiable-secret-sharing","display_name":"Verifiable secret sharing","score":0.6842986345291138},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6109112501144409},{"id":"https://openalex.org/keywords/arbitrary-precision-arithmetic","display_name":"Arbitrary-precision arithmetic","score":0.5773757696151733},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.512834370136261},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4694713354110718},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4592764973640442},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3621530532836914},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.09804412722587585},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07672077417373657}],"concepts":[{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.7969383597373962},{"id":"https://openalex.org/C85847156","wikidata":"https://www.wikidata.org/wiki/Q59015987","display_name":"Verifiable secret sharing","level":3,"score":0.6842986345291138},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6109112501144409},{"id":"https://openalex.org/C83581934","wikidata":"https://www.wikidata.org/wiki/Q527381","display_name":"Arbitrary-precision arithmetic","level":2,"score":0.5773757696151733},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.512834370136261},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4694713354110718},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4592764973640442},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3621530532836914},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.09804412722587585},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07672077417373657},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C19165224","wikidata":"https://www.wikidata.org/wiki/Q23404","display_name":"Anthropology","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/0004-3702(88)90061-6","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0004-3702(88)90061-6","pdf_url":null,"source":{"id":"https://openalex.org/S196139623","display_name":"Artificial Intelligence","issn_l":"0004-3702","issn":["0004-3702","1872-7921"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Artificial Intelligence","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W2038730428","https://openalex.org/W2052165970","https://openalex.org/W2157266306","https://openalex.org/W6659844971","https://openalex.org/W6678133649"],"related_works":["https://openalex.org/W2087454352","https://openalex.org/W1656092346","https://openalex.org/W2073476805","https://openalex.org/W2037029451","https://openalex.org/W4245068234","https://openalex.org/W1531645310","https://openalex.org/W2435153186","https://openalex.org/W2391934197","https://openalex.org/W2156774177","https://openalex.org/W2181927644"],"abstract_inverted_index":null,"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}