{"id":"https://openalex.org/W2912842130","doi":"https://doi.org/10.1145/3326229.3326252","title":"Plantinga-Vegter Algorithm takes Average Polynomial Time","display_name":"Plantinga-Vegter Algorithm takes Average Polynomial Time","publication_year":2019,"publication_date":"2019-07-08","ids":{"openalex":"https://openalex.org/W2912842130","doi":"https://doi.org/10.1145/3326229.3326252","mag":"2912842130"},"language":"en","primary_location":{"id":"doi:10.1145/3326229.3326252","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3326229.3326252","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2019 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1901.09234","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079608792","display_name":"Felipe Cucker","orcid":"https://orcid.org/0000-0002-4569-3248"},"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":true,"raw_author_name":"Felipe Cucker","raw_affiliation_strings":["City University of Hong Kong, Hong Kong, Hong Kong"],"affiliations":[{"raw_affiliation_string":"City University of Hong Kong, Hong Kong, Hong Kong","institution_ids":["https://openalex.org/I168719708"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015984499","display_name":"Alperen A. Erg\u00fcr","orcid":"https://orcid.org/0000-0002-2340-6551"},"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":"Alperen A. Erg\u00fcr","raw_affiliation_strings":["Technische Universit\u00e4t Berlin, Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Technische Universit\u00e4t Berlin, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021775859","display_name":"Josu\u00e9 Tonelli-Cueto","orcid":"https://orcid.org/0000-0002-2904-1215"},"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":"Josue Tonelli-Cueto","raw_affiliation_strings":["Technische Universit\u00e4t Berlin, Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Technische Universit\u00e4t Berlin, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5079608792"],"corresponding_institution_ids":["https://openalex.org/I168719708"],"apc_list":null,"apc_paid":null,"fwci":1.7498,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.82663241,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"114","last_page":"121"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9998000264167786,"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":0.9998000264167786,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9833999872207642,"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":0.9754999876022339,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6034319400787354},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5722631812095642},{"id":"https://openalex.org/keywords/probabilistic-analysis-of-algorithms","display_name":"Probabilistic analysis of algorithms","score":0.5424805879592896},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5319680571556091},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.49918460845947266},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.49257737398147583},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47227439284324646},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.46727192401885986},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4657597839832306},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4614087641239166},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.4260575771331787},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3618786334991455},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33779847621917725},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12305918335914612}],"concepts":[{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6034319400787354},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5722631812095642},{"id":"https://openalex.org/C24404364","wikidata":"https://www.wikidata.org/wiki/Q7246846","display_name":"Probabilistic analysis of algorithms","level":3,"score":0.5424805879592896},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5319680571556091},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.49918460845947266},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.49257737398147583},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47227439284324646},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.46727192401885986},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4657597839832306},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4614087641239166},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.4260575771331787},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3618786334991455},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33779847621917725},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12305918335914612},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/3326229.3326252","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3326229.3326252","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2019 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1901.09234","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1901.09234","pdf_url":"https://arxiv.org/pdf/1901.09234","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-05526020v1","is_oa":true,"landing_page_url":"https://hal.science/hal-05526020","pdf_url":"https://hal.science/hal-05526020v1/file/1901.09234v2.pdf","source":{"id":"https://openalex.org/S4406922461","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSAC '19: International Symposium on Symbolic and Algebraic Computation, ACM SIGSAM, Jul 2019, Beijing China, China. pp.114-121, &#x27E8;10.1145/3326229.3326252&#x27E9;","raw_type":"Conference papers"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1901.09234","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1901.09234","pdf_url":"https://arxiv.org/pdf/1901.09234","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":[{"id":"https://openalex.org/F4320309893","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23"},{"id":"https://openalex.org/F4320323688","display_name":"Einstein Stiftung Berlin","ror":"https://ror.org/03s0fv852"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W203551860","https://openalex.org/W1559487075","https://openalex.org/W2002728800","https://openalex.org/W2021592149","https://openalex.org/W2033943710","https://openalex.org/W2034053794","https://openalex.org/W2074068518","https://openalex.org/W2081131431","https://openalex.org/W2089028133","https://openalex.org/W2118625817","https://openalex.org/W2120694921","https://openalex.org/W2129635337","https://openalex.org/W2309534700","https://openalex.org/W2556509938","https://openalex.org/W2619629350","https://openalex.org/W2640923064","https://openalex.org/W2787248994","https://openalex.org/W2890941494","https://openalex.org/W2962738866","https://openalex.org/W2962955948","https://openalex.org/W2963720619","https://openalex.org/W3101405261","https://openalex.org/W3103556238","https://openalex.org/W3106149501","https://openalex.org/W3123452453","https://openalex.org/W4250954493","https://openalex.org/W4254852607","https://openalex.org/W4289920060","https://openalex.org/W4300127518","https://openalex.org/W4300873693"],"related_works":["https://openalex.org/W2399035783","https://openalex.org/W3161230432","https://openalex.org/W4367190712","https://openalex.org/W2168900540","https://openalex.org/W1487201914","https://openalex.org/W2144537400","https://openalex.org/W4234010763","https://openalex.org/W2163083173","https://openalex.org/W1970614317","https://openalex.org/W2142565884"],"abstract_inverted_index":{"We":[0,103,145],"exhibit":[1,105],"a":[2,31,81,106,150],"condition-based":[3],"analysis":[4,18,108,130],"of":[5,19,64,84,90,109,153],"the":[6,20,61,65,86,91,110,135,156],"adaptive":[7],"subdivision":[8],"algorithm":[9,66],"due":[10,23],"to":[11,24,80,159],"Plantinga":[12],"and":[13,27,134,143],"Vegter.":[14],"The":[15],"first":[16],"complexity":[17,89,115],"\\pv~Algorithm":[21,92,111],"is":[22,56,93],"Burr,":[25,141],"Gao":[26],"Tsigaridas":[28],"who":[29],"proved":[30],"\\mathcalO":[32],"\\big(2^\u03c4":[33],"d^4":[34],"\u0142og":[35],"d":[36,43],"\\big)":[37],"worst-case":[38],"cost":[39],"bound":[40],"for":[41,97],"degree":[42,99],"plane":[44,101],"curves":[45],"with":[46,60,72,78,131],"maximum":[47],"coefficient":[48],"bit-size~\u03c4.":[49],"This":[50],"exponential":[51],"bound,":[52],"it":[53],"was":[54],"observed,":[55],"in":[57,67,70],"stark":[58],"contrast":[59],"good":[62],"performance":[63],"practice.":[68],"More":[69],"line":[71],"this":[73,147],"performance,":[74],"we":[75,121],"show":[76],"that,":[77],"respect":[79],"broad":[82],"family":[83],"measures,":[85],"expected":[87],"time":[88],"bounded":[94],"by":[95,140],"O(d^7)":[96],"real,":[98],"d,":[100],"curves.":[102],"also":[104],"smoothed":[107],"that":[112],"yields":[113],"similar":[114],"estimates.":[116],"To":[117],"obtain":[118],"these":[119],"results":[120],"combine":[122],"robust":[123],"probabilistic":[124],"techniques":[125],"coming":[126],"from":[127],"geometric":[128],"functional":[129],"condition":[132],"numbers":[133],"continuous":[136],"amortization":[137],"paradigm":[138],"introduced":[139],"Krahmer":[142],"Yap.":[144],"hope":[146],"will":[148],"motivate":[149],"fruitful":[151],"exchange":[152],"ideas":[154],"between":[155],"different":[157],"approaches":[158],"numerical":[160],"computation.":[161]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-03T22:45:19.894376","created_date":"2020-11-23T00:00:00"}
