{"id":"https://openalex.org/W2187292610","doi":"https://doi.org/10.4086/toc.2013.v009a020","title":"","display_name":"","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2187292610","doi":"https://doi.org/10.4086/toc.2013.v009a020","mag":"2187292610"},"language":"en","primary_location":{"id":"doi:10.4086/toc.2013.v009a020","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2013.v009a020","pdf_url":"https://theoryofcomputing.org/articles/v009a020/v009a020.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":"https://theoryofcomputing.org/articles/v009a020/v009a020.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079755716","display_name":"Alexander A. Sherstov","orcid":"https://orcid.org/0000-0002-2488-7852"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Alexander A. Sherstov","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5079755716"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.9589,"has_fulltext":true,"cited_by_count":26,"citation_normalized_percentile":{"value":0.9146762,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"9","issue":"1","first_page":"653","last_page":"663"},"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9995999932289124,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9962000250816345,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.8338634967803955},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7975211143493652},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.7715521454811096},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6991063952445984},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6281416416168213},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.5697486400604248},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5647805333137512},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.513093113899231},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4846942722797394},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1486024260520935},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11109796166419983}],"concepts":[{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.8338634967803955},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7975211143493652},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.7715521454811096},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6991063952445984},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6281416416168213},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.5697486400604248},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5647805333137512},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.513093113899231},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4846942722797394},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1486024260520935},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11109796166419983},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.4086/toc.2013.v009a020","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2013.v009a020","pdf_url":"https://theoryofcomputing.org/articles/v009a020/v009a020.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.2013.v009a020","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2013.v009a020","pdf_url":"https://theoryofcomputing.org/articles/v009a020/v009a020.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/G1171700966","display_name":null,"funder_award_id":"NSF CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2629604219","display_name":null,"funder_award_id":"CCF-1149018","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3041994311","display_name":null,"funder_award_id":"14901","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3658206218","display_name":"CAREER: Limits of Communication","funder_award_id":"1149018","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","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"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2187292610.pdf","grobid_xml":"https://content.openalex.org/works/W2187292610.grobid-xml"},"referenced_works_count":49,"referenced_works":["https://openalex.org/W24307859","https://openalex.org/W1517311456","https://openalex.org/W1609370892","https://openalex.org/W1618756527","https://openalex.org/W1662824729","https://openalex.org/W1838647306","https://openalex.org/W1964537764","https://openalex.org/W1969865855","https://openalex.org/W1973728061","https://openalex.org/W1979124844","https://openalex.org/W2000070319","https://openalex.org/W2010501977","https://openalex.org/W2012496360","https://openalex.org/W2023316152","https://openalex.org/W2031374990","https://openalex.org/W2034038586","https://openalex.org/W2044859592","https://openalex.org/W2053590396","https://openalex.org/W2062223744","https://openalex.org/W2077740213","https://openalex.org/W2086789740","https://openalex.org/W2091623775","https://openalex.org/W2093796999","https://openalex.org/W2104038652","https://openalex.org/W2106458073","https://openalex.org/W2107923128","https://openalex.org/W2112553910","https://openalex.org/W2114522915","https://openalex.org/W2115407783","https://openalex.org/W2117822564","https://openalex.org/W2122780600","https://openalex.org/W2127259150","https://openalex.org/W2129275337","https://openalex.org/W2134974549","https://openalex.org/W2138096767","https://openalex.org/W2146956300","https://openalex.org/W2147154704","https://openalex.org/W2148211896","https://openalex.org/W2150157290","https://openalex.org/W2158416399","https://openalex.org/W2166652312","https://openalex.org/W2173499948","https://openalex.org/W2593070235","https://openalex.org/W2610386774","https://openalex.org/W2611287588","https://openalex.org/W2611310478","https://openalex.org/W2611933946","https://openalex.org/W2963914453","https://openalex.org/W4226347946"],"related_works":["https://openalex.org/W238609530","https://openalex.org/W2734192830","https://openalex.org/W3016395638","https://openalex.org/W1636163329","https://openalex.org/W4292947165","https://openalex.org/W3045121788","https://openalex.org/W3201655533","https://openalex.org/W3134442314","https://openalex.org/W2281248943","https://openalex.org/W4367190712"],"abstract_inverted_index":{"The":[0,90],"approximate":[1,43,83],"degree":[2,11,44,84],"of":[3,12,55],"a":[4,13,53],"Boolean":[5],"function":[6,28,74],"f":[7,18],"is":[8,49,88],"the":[9,27,39,58,60,73],"least":[10],"real":[14],"polynomial":[15],"that":[16,26,72],"approximates":[17],"within":[19],"1/3":[20],"at":[21],"every":[22],"point.":[23],"We":[24],"prove":[25,71],"n":[29,31,77],"i=1":[30,76],"j=1":[32,78],"x":[33,79],"i":[34,80],"j":[35,81],",":[36],"known":[37],"as":[38],"AND-OR":[40],"tree,":[41],"has":[42,82],"(n).":[45],"This":[46],"lower":[47,92],"bound":[48,63,93],"tight":[50],"and":[51,99],"closes":[52],"line":[54],"research":[56],"on":[57],"problem,":[59],"best":[61],"previous":[62],"being":[64],"(n":[65],"0.75":[66],").":[67],"More":[68],"generally,":[69],"we":[70],"m":[75],"(":[85],"mn),":[86],"which":[87],"tight.":[89],"same":[91],"was":[94],"obtained":[95],"independently":[96],"by":[97],"Bun":[98],"Thaler":[100],"(2013)":[101],"using":[102],"related":[103],"techniques.":[104]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2016-06-24T00:00:00"}
