{"id":"https://openalex.org/W3001841464","doi":"https://doi.org/10.4086/toc.2019.v015a021","title":"","display_name":"","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W3001841464","doi":"https://doi.org/10.4086/toc.2019.v015a021","mag":"3001841464"},"language":"en","primary_location":{"id":"doi:10.4086/toc.2019.v015a021","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2019.v015a021","pdf_url":"http://www.theoryofcomputing.org/articles/v015a021/v015a021.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"http://www.theoryofcomputing.org/articles/v015a021/v015a021.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008689083","display_name":"Nikhil Bansal","orcid":"https://orcid.org/0000-0002-6290-0894"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Nikhil Bansal","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044591096","display_name":"Daniel Dadush","orcid":"https://orcid.org/0000-0001-5577-5012"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Daniel Dadush","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5114033528","display_name":"Shashwat Garg","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shashwat Garg","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5044999305","display_name":"Shachar Lovett","orcid":"https://orcid.org/0000-0003-4552-1443"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shachar Lovett","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5008689083"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.9469,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.86154554,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"15","issue":"1","first_page":"1","last_page":"27"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9921000003814697,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9921000003814697,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9003000259399414,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/mathematics","display_name":"Mathematics","score":0.6392219662666321},{"id":"https://openalex.org/keywords/gaussian-measure","display_name":"Gaussian measure","score":0.5787981152534485},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5517397522926331},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5417234897613525},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.5329039692878723},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.49398380517959595},{"id":"https://openalex.org/keywords/randomized-algorithm","display_name":"Randomized algorithm","score":0.4851852059364319},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.47550731897354126},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.4610075354576111},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4231802821159363},{"id":"https://openalex.org/keywords/convex-body","display_name":"Convex body","score":0.41821396350860596},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4174973666667938},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.3964332342147827},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.27383339405059814},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20679107308387756},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07561314105987549},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07380229234695435}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6392219662666321},{"id":"https://openalex.org/C2777630202","wikidata":"https://www.wikidata.org/wiki/Q5527840","display_name":"Gaussian measure","level":3,"score":0.5787981152534485},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5517397522926331},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5417234897613525},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.5329039692878723},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.49398380517959595},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.4851852059364319},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.47550731897354126},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4610075354576111},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4231802821159363},{"id":"https://openalex.org/C134912446","wikidata":"https://www.wikidata.org/wiki/Q5166516","display_name":"Convex body","level":4,"score":0.41821396350860596},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4174973666667938},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.3964332342147827},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.27383339405059814},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20679107308387756},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07561314105987549},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07380229234695435},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.4086/toc.2019.v015a021","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2019.v015a021","pdf_url":"http://www.theoryofcomputing.org/articles/v015a021/v015a021.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.4086/toc.2019.v015a021","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2019.v015a021","pdf_url":"http://www.theoryofcomputing.org/articles/v015a021/v015a021.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1499980992","display_name":null,"funder_award_id":"639.071.510","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G3127164406","display_name":null,"funder_award_id":"CCF award 1614023","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4405413375","display_name":null,"funder_award_id":"639.023.812","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G6507447573","display_name":null,"funder_award_id":"several","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6823996144","display_name":null,"funder_award_id":"022.005.0","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G7157536220","display_name":null,"funder_award_id":"022.005.025","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G8333547667","display_name":null,"funder_award_id":"VICI grant 639.023.812","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G842637274","display_name":null,"funder_award_id":"1614023","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/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3001841464.pdf","grobid_xml":"https://content.openalex.org/works/W3001841464.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W35105443","https://openalex.org/W1972194652","https://openalex.org/W2007604989","https://openalex.org/W2011095973","https://openalex.org/W2035339061","https://openalex.org/W2065609263","https://openalex.org/W2077872360","https://openalex.org/W2080024126","https://openalex.org/W2080064821","https://openalex.org/W2083459869","https://openalex.org/W2084471691","https://openalex.org/W2088402854","https://openalex.org/W2097240805","https://openalex.org/W2113174542","https://openalex.org/W2127125853","https://openalex.org/W2140322654","https://openalex.org/W2144407406","https://openalex.org/W2149178517","https://openalex.org/W2191437688","https://openalex.org/W2240692020","https://openalex.org/W2342483111","https://openalex.org/W2467941010","https://openalex.org/W2493844837","https://openalex.org/W2551238896","https://openalex.org/W2552451242","https://openalex.org/W2558885861","https://openalex.org/W2562861483","https://openalex.org/W2593701861","https://openalex.org/W2744926673","https://openalex.org/W2913359901","https://openalex.org/W2942921462","https://openalex.org/W2963043279","https://openalex.org/W2963978809","https://openalex.org/W2964024102","https://openalex.org/W4226347946","https://openalex.org/W4249137521","https://openalex.org/W4254343065","https://openalex.org/W4255357113","https://openalex.org/W4381304672"],"related_works":["https://openalex.org/W3173366859","https://openalex.org/W4234010763","https://openalex.org/W4307416302","https://openalex.org/W4313227037","https://openalex.org/W339301305","https://openalex.org/W2913308506","https://openalex.org/W2097240805","https://openalex.org/W2565109825","https://openalex.org/W2091573779","https://openalex.org/W2621997583"],"abstract_inverted_index":{"A":[0],"classic":[1],"result":[2,55],"of":[3,33,44,53,86],"Banaszczyk":[4],"(Random":[5],"Str.":[6],"&":[7],"Algor.":[8],"1997)":[9],"states":[10],"that":[11,47],"given":[12],"any":[13,26],"n":[14],"vectors":[15,46,88],"in":[16,30,49,69,91,109],"R":[17,31],"m":[18,32],"with":[19],"2":[20],"-norm":[21],"at":[22,36],"most":[23],"1":[24,42,67,84],"and":[25,58],"convex":[27],"body":[28],"K":[29],"Gaussian":[34],"measure":[35],"least":[37],"half,":[38],"there":[39],"exists":[40],"a":[41,66,83],"combination":[43,68,85],"these":[45],"lies":[48,90],"5K.":[50],"Banaszczyk's":[51],"proof":[52],"this":[54,73],"was":[56,60],"non-constructive":[57],"it":[59],"open":[61],"how":[62],"to":[63,81,102],"find":[64,82],"such":[65],"polynomial":[70],"time.":[71],"In":[72],"paper,":[74],"we":[75],"give":[76],"an":[77],"efficient":[78,104],"randomized":[79],"algorithm":[80],"the":[87],"which":[89],"cK":[92],"for":[93,106],"some":[94],"fixed":[95],"constant":[96],"c":[97],">":[98],"0.":[99],"This":[100],"leads":[101],"new":[103],"algorithms":[105],"several":[107],"problems":[108],"discrepancy":[110],"theory.":[111]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-11T08:14:18.477133","created_date":"2020-01-30T00:00:00"}