{"id":"https://openalex.org/W3085327550","doi":"https://doi.org/10.1137/20m1385287","title":"Smoothing the Gap Between NP and ER","display_name":"Smoothing the Gap Between NP and ER","publication_year":2022,"publication_date":"2022-04-07","ids":{"openalex":"https://openalex.org/W3085327550","doi":"https://doi.org/10.1137/20m1385287","mag":"3085327550"},"language":"en","primary_location":{"id":"doi:10.1137/20m1385287","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1385287","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":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://dspace.library.uu.nl/handle/1874/431856","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042187195","display_name":"Jeff Erickson","orcid":"https://orcid.org/0000-0002-5253-2282"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jeff Erickson","raw_affiliation_strings":["***University of Illinois at Urbana-Champaign"],"affiliations":[{"raw_affiliation_string":"***University of Illinois at Urbana-Champaign","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009550388","display_name":"Ivor van der Hoog","orcid":"https://orcid.org/0009-0006-2624-0231"},"institutions":[{"id":"https://openalex.org/I193662353","display_name":"Utrecht University","ror":"https://ror.org/04pp8hn57","country_code":"NL","type":"education","lineage":["https://openalex.org/I193662353"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Ivor van der Hoog","raw_affiliation_strings":["Utrecht University"],"affiliations":[{"raw_affiliation_string":"Utrecht University","institution_ids":["https://openalex.org/I193662353"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077251333","display_name":"Tillmann Miltzow","orcid":"https://orcid.org/0000-0003-4563-2864"},"institutions":[{"id":"https://openalex.org/I193662353","display_name":"Utrecht University","ror":"https://ror.org/04pp8hn57","country_code":"NL","type":"education","lineage":["https://openalex.org/I193662353"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Tillmann Miltzow","raw_affiliation_strings":["Utrecht University"],"affiliations":[{"raw_affiliation_string":"Utrecht University","institution_ids":["https://openalex.org/I193662353"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5042187195"],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":null,"apc_paid":null,"fwci":1.3574,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.8213441,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"53","issue":"6","first_page":"FOCS20","last_page":"102"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998000264167786,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998000264167786,"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":0.9994000196456909,"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"}},{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9994000196456909,"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/mathematics","display_name":"Mathematics","score":0.5908635854721069},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5405035018920898},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5297955870628357},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.48834535479545593},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4591718018054962},{"id":"https://openalex.org/keywords/existential-quantification","display_name":"Existential quantification","score":0.4545828104019165},{"id":"https://openalex.org/keywords/complexity-class","display_name":"Complexity class","score":0.4262276291847229},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4050635099411011},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2648562788963318}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5908635854721069},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5405035018920898},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5297955870628357},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.48834535479545593},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4591718018054962},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.4545828104019165},{"id":"https://openalex.org/C39637292","wikidata":"https://www.wikidata.org/wiki/Q908207","display_name":"Complexity class","level":3,"score":0.4262276291847229},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4050635099411011},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2648562788963318},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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":3,"locations":[{"id":"doi:10.1137/20m1385287","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1385287","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":"pmh:oai:dspace.library.uu.nl:1874/431856","is_oa":true,"landing_page_url":"https://dspace.library.uu.nl/handle/1874/431856","pdf_url":null,"source":{"id":"https://openalex.org/S4306401649","display_name":"Utrecht University Repository (Utrecht University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I193662353","host_organization_name":"Utrecht University","host_organization_lineage":["https://openalex.org/I193662353"],"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":null,"raw_type":"/dk/atira/pure/researchoutput/researchoutputtypes/workingpaper/preprint"},{"id":"pmh:oai:dspace.library.uu.nl:1874/475183","is_oa":true,"landing_page_url":"https://dspace.library.uu.nl/handle/1874/475183","pdf_url":null,"source":{"id":"https://openalex.org/S4306401649","display_name":"Utrecht University Repository (Utrecht University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I193662353","host_organization_name":"Utrecht University","host_organization_lineage":["https://openalex.org/I193662353"],"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":null,"raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:dspace.library.uu.nl:1874/431856","is_oa":true,"landing_page_url":"https://dspace.library.uu.nl/handle/1874/431856","pdf_url":null,"source":{"id":"https://openalex.org/S4306401649","display_name":"Utrecht University Repository (Utrecht University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I193662353","host_organization_name":"Utrecht University","host_organization_lineage":["https://openalex.org/I193662353"],"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":null,"raw_type":"/dk/atira/pure/researchoutput/researchoutputtypes/workingpaper/preprint"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1341482105","display_name":null,"funder_award_id":"614.001.504","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G5972929827","display_name":null,"funder_award_id":"016.Veni.192.25","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":69,"referenced_works":["https://openalex.org/W41260695","https://openalex.org/W94985437","https://openalex.org/W134510267","https://openalex.org/W176071698","https://openalex.org/W1483218536","https://openalex.org/W1503030630","https://openalex.org/W1519444547","https://openalex.org/W1542553486","https://openalex.org/W1550331971","https://openalex.org/W1552810675","https://openalex.org/W1556128689","https://openalex.org/W1571051474","https://openalex.org/W1602434374","https://openalex.org/W1607888378","https://openalex.org/W1874694348","https://openalex.org/W1964080182","https://openalex.org/W1968264007","https://openalex.org/W1969514863","https://openalex.org/W1981172165","https://openalex.org/W1985361644","https://openalex.org/W1986405515","https://openalex.org/W1992578441","https://openalex.org/W1996028864","https://openalex.org/W2005314985","https://openalex.org/W2006753964","https://openalex.org/W2007458506","https://openalex.org/W2019110169","https://openalex.org/W2030844359","https://openalex.org/W2034053794","https://openalex.org/W2036265926","https://openalex.org/W2038280788","https://openalex.org/W2041495686","https://openalex.org/W2043552663","https://openalex.org/W2050761777","https://openalex.org/W2063402394","https://openalex.org/W2068497209","https://openalex.org/W2071846104","https://openalex.org/W2074286662","https://openalex.org/W2074843875","https://openalex.org/W2102167981","https://openalex.org/W2117427692","https://openalex.org/W2131662609","https://openalex.org/W2148713284","https://openalex.org/W2164485560","https://openalex.org/W2234020812","https://openalex.org/W2301555989","https://openalex.org/W2319466955","https://openalex.org/W2403232853","https://openalex.org/W2469655323","https://openalex.org/W2482552401","https://openalex.org/W2566164082","https://openalex.org/W2593618663","https://openalex.org/W2612212426","https://openalex.org/W2745281314","https://openalex.org/W2770074417","https://openalex.org/W2792901515","https://openalex.org/W2899198588","https://openalex.org/W2950863166","https://openalex.org/W2963527881","https://openalex.org/W2963616416","https://openalex.org/W2963878374","https://openalex.org/W2964729910","https://openalex.org/W2971120546","https://openalex.org/W3037769165","https://openalex.org/W3105946615","https://openalex.org/W3128545493","https://openalex.org/W3160805239","https://openalex.org/W4255213956","https://openalex.org/W4301168154"],"related_works":["https://openalex.org/W297598734","https://openalex.org/W1504200807","https://openalex.org/W2086025566","https://openalex.org/W1702487489","https://openalex.org/W2132910148","https://openalex.org/W2042051386","https://openalex.org/W270168689","https://openalex.org/W113209803","https://openalex.org/W2104611150","https://openalex.org/W1629505938"],"abstract_inverted_index":{"We":[0,312,328,384],"study":[1,321],"algorithmic":[2],"problems":[3,50,147,181,324,393,421],"that":[4,64,66,116,162,182,214,271,282,330,363],"belong":[5],"to":[6,228,254,265,277,316,320,388,420],"the":[7,11,15,30,35,54,67,100,107,159,163,166,208,215,223,240,266,364,396,402,409,431],"complexity":[8,86],"class":[9,87,334],"of":[10,14,34,62,71,97,110,165,217,239,256,295,335,381,404,426],"existential":[12,32],"theory":[13,33],"reals":[16,36],"($\\exists":[17],"\\mathbb{R}$).":[18],"A":[19],"problem":[20,31,101,224,411],"is":[21,26,90,134,141,190,194,203,226,275],"\\ensuremath\\exists":[22,296],"\\mathbbR-complete":[23],"if":[24,39,196],"it":[25,40,193],"as":[27,29,44,106,298,401],"hard":[28],"(ETR)":[37],"and":[38,69,80,120,132,368],"can":[41,74,103,118,124,341],"be":[42,75,104,255,342],"written":[43],"an":[45,149,156,292],"ETR":[46,102,189,310],"formula.":[47],"Traditionally,":[48],"these":[49],"are":[51,186,305],"studied":[52],"in":[53,77,121,129,178,199,284,359,412],"real":[55,94,113,262,288,303,353],"random":[56],"access":[57],"machine":[58],"(RAM),":[59],"a":[60,93,218,236,249,261,279,287,302,318,332,360,423],"model":[61],"computation":[63],"assumes":[65],"storage":[68],"comparison":[70],"real-valued":[72,108],"numbers":[73],"done":[76],"constant":[78,130],"space":[79,131],"time,":[81],"with":[82,344,422],"infinite":[83],"precision.":[84],"The":[85,112,180,231],"$\\exists":[88,145,272,322,336,369,390],"\\mathbb{R}$":[89,273,370],"often":[91,204],"called":[92],"RAM":[95,114,263,304,354],"analogue":[96,264],"NP,":[98],"since":[99,143],"viewed":[105],"variant":[109],"SAT.":[111],"assumption":[115,140],"we":[117,123,246,252,259],"represent":[119],"which":[122,171,212,251,269,394],"compare":[125],"arbitrary":[126],"irrational":[127],"values":[128],"time":[133],"not":[135],"very":[136],"realistic.":[137],"Yet":[138],"this":[139,184,244,314],"vital,":[142],"some":[144],"\\mathbb{R}$-complete":[146,323,337,391],"have":[148,395],"\u201cexponential":[150],"bit":[151,233,398],"phenomenon,\u201d":[152],"where":[153],"there":[154],"exists":[155],"input":[157],"for":[158,222,331],"problem,":[160],"such":[161,400],"witness":[164,225,340,376],"solution":[167,375],"requires":[168],"geometric":[169],"coordinates":[170],"need":[172],"exponential":[173,232,397],"word":[174],"size":[175],"when":[176],"represented":[177,343],"binary.":[179],"exhibit":[183],"phenomenon":[185,234,399],"NP-hard":[187],"(since":[188],"NP-hard)":[191],"but":[192],"unknown":[195],"they":[197],"lie":[198],"NP.":[200],"NP":[201,229,367],"membership":[202,274],"showed":[205],"by":[206,347,372],"using":[207,348],"famous":[209],"Cook--Levin":[210,241,267],"theorem,":[211],"states":[213],"existence":[216],"polynomial-time":[219,285],"verification":[220,280,299,355],"algorithm":[221,281],"equivalent":[227,276],"membership.":[230],"prohibits":[235],"straightforward":[237],"application":[238],"theorem.":[242],"In":[243],"paper":[245],"first":[247],"present":[248],"result":[250,315],"believe":[253],"independent":[257],"interest:":[258],"prove":[260],"theorem":[268],"shows":[270,358],"having":[278],"runs":[283],"on":[286,301,351],"RAM.":[289],"This":[290,357],"gives":[291],"easy":[293],"proof":[294],"\\mathbbR-membership,":[297],"algorithms":[300],"much":[306],"more":[307],"versatile":[308],"than":[309],"formulas.":[311],"use":[313],"construct":[317],"framework":[319,387],"under":[325],"smoothed":[326,349],"analysis.":[327],"show":[329],"wide":[333],"problems,":[338],"its":[339,352],"logarithmic":[345],"input-precision":[346],"analysis":[350],"algorithm.":[356],"formal":[361],"way":[362],"boundary":[365],"between":[366],"(formed":[371],"inputs":[373],"whose":[374],"needs":[377],"high":[378],"input-precision)":[379],"consists":[380],"contrived":[382],"input.":[383],"apply":[385],"our":[386,416],"well-studied":[389],"recognition":[392,403],"realizable":[405],"order":[406],"types":[407],"or":[408],"Steinitz":[410],"fixed":[413],"dimension.":[414],"Interestingly":[415],"techniques":[417],"also":[418],"generalize":[419],"natural":[424],"notion":[425],"resource":[427],"augmentation":[428],"(geometric":[429],"packing,":[430],"art":[432],"gallery":[433],"problem).":[434]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
