{"id":"https://openalex.org/W2949104552","doi":"https://doi.org/10.1137/19m1268550","title":"Efficient Algorithm for Generalized Polynomial Partitioning and Its Applications","display_name":"Efficient Algorithm for Generalized Polynomial Partitioning and Its Applications","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W2949104552","doi":"https://doi.org/10.1137/19m1268550","mag":"2949104552"},"language":"en","primary_location":{"id":"doi:10.1137/19m1268550","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1268550","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":"preprint","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://export.arxiv.org/pdf/1812.10269","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058649592","display_name":"Pankaj K. Agarwal","orcid":"https://orcid.org/0000-0002-9439-181X"},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pankaj K. Agarwal","raw_affiliation_strings":["Duke University#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Duke University#TAB#","institution_ids":["https://openalex.org/I170897317"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042232059","display_name":"Boris Aronov","orcid":"https://orcid.org/0000-0003-3110-4702"},"institutions":[{"id":"https://openalex.org/I102475099","display_name":"Sup\u00e9lec","ror":"https://ror.org/00n7gwn90","country_code":"FR","type":"education","lineage":["https://openalex.org/I102475099"]},{"id":"https://openalex.org/I15196421","display_name":"University of Applied Sciences and Arts of Southern Switzerland","ror":"https://ror.org/05ep8g269","country_code":"CH","type":"education","lineage":["https://openalex.org/I15196421"]},{"id":"https://openalex.org/I4210102264","display_name":"Shandong University of Political Science and Law","ror":"https://ror.org/01b2j5886","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210102264"]}],"countries":["CH","CN","FR"],"is_corresponding":false,"raw_author_name":"Boris Aronov","raw_affiliation_strings":["New York University<sup>**</sup>"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"New York University<sup>**</sup>","institution_ids":["https://openalex.org/I15196421","https://openalex.org/I4210102264","https://openalex.org/I102475099"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089313525","display_name":"Esther Ezra","orcid":"https://orcid.org/0000-0001-8133-1335"},"institutions":[{"id":"https://openalex.org/I13955877","display_name":"Bar-Ilan University","ror":"https://ror.org/03kgsv495","country_code":"IL","type":"education","lineage":["https://openalex.org/I13955877"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Esther Ezra","raw_affiliation_strings":["Bar-Ilan University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bar-Ilan University","institution_ids":["https://openalex.org/I13955877"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078560468","display_name":"Joshua Zahl","orcid":"https://orcid.org/0000-0001-5129-8300"},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Joshua Zahl","raw_affiliation_strings":[", University of British Columbia"],"raw_orcid":"https://orcid.org/0000-0001-5129-8300","affiliations":[{"raw_affiliation_string":", University of British Columbia","institution_ids":["https://openalex.org/I141945490"]}]}],"institutions":[],"countries_distinct_count":6,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00607323,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"50","issue":"2","first_page":"760","last_page":"787"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998999834060669,"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":0.9998999834060669,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9986000061035156,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/combinatorics","display_name":"Combinatorics","score":0.6920569539070129},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.6483141779899597},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6164538264274597},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5816922783851624},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5731472373008728},{"id":"https://openalex.org/keywords/quantifier-elimination","display_name":"Quantifier elimination","score":0.5531441569328308},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.49028828740119934},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4264790415763855},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42167600989341736},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.41808146238327026},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1434432864189148},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08078676462173462}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6920569539070129},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.6483141779899597},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6164538264274597},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5816922783851624},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5731472373008728},{"id":"https://openalex.org/C32278780","wikidata":"https://www.wikidata.org/wiki/Q1849020","display_name":"Quantifier elimination","level":2,"score":0.5531441569328308},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.49028828740119934},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4264790415763855},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42167600989341736},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.41808146238327026},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1434432864189148},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08078676462173462},{"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/19m1268550","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1268550","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":"mag:2949104552","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1812.10269","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1812.10269","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1812.10269","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"mag:2949104552","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1812.10269","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1818401345","display_name":null,"funder_award_id":"CCF-15-46392","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G1969041588","display_name":null,"funder_award_id":"824/17","funder_id":"https://openalex.org/F4320320950","funder_display_name":"United States-Israel Binational Science Foundation"},{"id":"https://openalex.org/G3488816049","display_name":null,"funder_award_id":"CCF-15-13816","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G415145287","display_name":null,"funder_award_id":"2014/170","funder_id":"https://openalex.org/F4320320950","funder_display_name":"United States-Israel Binational Science Foundation"},{"id":"https://openalex.org/G4252697786","display_name":null,"funder_award_id":"W911NF-15-1-0408","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G4310336233","display_name":null,"funder_award_id":"CCF-12-18791","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4707214446","display_name":null,"funder_award_id":"2012/229","funder_id":"https://openalex.org/F4320320950","funder_display_name":"United States-Israel Binational Science Foundation"},{"id":"https://openalex.org/G6395017990","display_name":null,"funder_award_id":"IIS-14-08846","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6531736302","display_name":null,"funder_award_id":"CCF:AF 1553354","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6744416296","display_name":null,"funder_award_id":"CCF-15-40656","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320950","display_name":"United States-Israel Binational Science Foundation","ror":"https://ror.org/00j8z2m73"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W596522316","https://openalex.org/W1574151794","https://openalex.org/W1621148473","https://openalex.org/W1862680590","https://openalex.org/W1966069213","https://openalex.org/W2029538739","https://openalex.org/W2058889860","https://openalex.org/W2062567923","https://openalex.org/W2067636581","https://openalex.org/W2100503751","https://openalex.org/W2101788557","https://openalex.org/W2144337080","https://openalex.org/W2149693294","https://openalex.org/W2150256023","https://openalex.org/W2295570425","https://openalex.org/W2343027471","https://openalex.org/W2568603896","https://openalex.org/W2751884597","https://openalex.org/W2906548559","https://openalex.org/W2963208722","https://openalex.org/W2963606251","https://openalex.org/W2995799124","https://openalex.org/W3043717872","https://openalex.org/W3102520527","https://openalex.org/W4238284510"],"related_works":["https://openalex.org/W2906548559","https://openalex.org/W2883277195","https://openalex.org/W3099419577","https://openalex.org/W2043648393","https://openalex.org/W2767086972","https://openalex.org/W2568071471","https://openalex.org/W3100802811","https://openalex.org/W2055334444","https://openalex.org/W2397130712","https://openalex.org/W1527447383","https://openalex.org/W3004632262","https://openalex.org/W2963409396","https://openalex.org/W1976601425","https://openalex.org/W3126911039","https://openalex.org/W3204151990","https://openalex.org/W3197561596","https://openalex.org/W3105711037","https://openalex.org/W2114430034","https://openalex.org/W2952889364","https://openalex.org/W3094484287"],"abstract_inverted_index":{"In":[0],"2015,":[1],"Guth":[2],"proved":[3],"that":[4,37,63,90,181,262],"if":[5,18],"$S$":[6],"is":[7,21,26,52,76,119,150,178,194,221,236],"a":[8,27,50,54,60,120,128,151,195,248,264],"collection":[9],"of":[10,31,41,73,85,91,98,114,130,146,189],"$n$":[11,253],"$g$-dimensional":[12],"semi-algebraic":[13,106,131,159,204],"sets":[14,46,107,132,205],"in":[15,78,108,133,135,161,163,206,208,229,243,258],"$\\mathbb{R}^d$":[16,134,162],"and":[17,142,170,185,215],"$D\\geq":[19],"1$":[20],"an":[22,96,179,222],"integer,":[23],"then":[24],"there":[25],"$d$-variate":[28],"polynomial":[29,51,103],"$P$":[30],"degree":[32],"at":[33],"most":[34],"$D$":[35],"so":[36],"each":[38],"connected":[39],"component":[40],"$\\mathbb{R}^d\\setminus":[42],"Z(P)$":[43],"intersects":[44],"$O(n/D^{d-g})$":[45],"from":[47],"$S$.":[48],"Such":[49],"called":[53],"generalized":[55],"partitioning":[56,104],"polynomial.":[57],"We":[58,93,110],"present":[59,95,111],"randomized":[61],"algorithm":[62,75,224,250],"computes":[64],"such":[65],"polynomials":[66],"efficiently":[67],"--":[68],"the":[69,83,186,190],"expected":[70,143,171,216],"running":[71],"time":[72,145],"our":[74,99,115],"linear":[77],"$|S|$.":[79],"Our":[80],"approach":[81],"exploits":[82],"technique":[84],"quantifier":[86],"elimination":[87],"combined":[88],"with":[89,139,158,167,212],"$\u03b5$-samples.":[92],"also":[94],"extension":[97],"construction":[100],"to":[101,251],"multi-level":[102],"for":[105,123,154,198,225,237],"$\\mathbb{R}^d$.":[109],"five":[112],"applications":[113],"result.":[116],"The":[117,148,192,219,233],"first":[118],"data":[121,152,196],"structure":[122,153,197],"answering":[124,155,199],"point-enclosure":[125],"queries":[126,157,202],"among":[127,203,241],"family":[129],"$O(\\log":[136,164],"n)$":[137,165,210],"time,":[138,166,173,211],"storage":[140,169,214],"complexity":[141,188],"preprocessing":[144,172,217],"$O(n^{d+\u03b5})$.":[147],"second":[149],"range-searching":[156],"ranges":[160],"$O(n^{t+\u03b5})$":[168],"where":[174,245],"$t":[175],"&gt;":[176],"0$":[177],"integer":[180],"depends":[182],"on":[183],"$d$":[184],"description":[187],"ranges.":[191],"third":[193],"vertical":[200],"ray-shooting":[201],"$\\mathbb{R}^{d}$":[207],"$O(\\log^2":[209],"$O(n^{d+\u03b5})$":[213],"time.":[218],"fourth":[220],"efficient":[223],"cutting":[226],"algebraic":[227],"curves":[228],"$\\mathbb{R}^2$":[230],"into":[231,260],"pseudo-segments.":[232],"fifth":[234],"application":[235],"eliminating":[238],"depth":[239,265],"cycles":[240],"triangles":[242,257],"$\\mathbb{R}^3$,":[244],"we":[246],"show":[247],"nearly-optimal":[249],"cut":[252],"pairwise":[254],"disjoint":[255],"non-vertical":[256],"$\\mathbb{R}^3$":[259],"pieces":[261],"form":[263],"order.":[266]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}