{"id":"https://openalex.org/W2020219958","doi":"https://doi.org/10.1137/s0097539792225935","title":"Closeness of NP-Hard Sets to Other Complexity Classes","display_name":"Closeness of NP-Hard Sets to Other Complexity Classes","publication_year":1994,"publication_date":"1994-04-01","ids":{"openalex":"https://openalex.org/W2020219958","doi":"https://doi.org/10.1137/s0097539792225935","mag":"2020219958"},"language":"en","primary_location":{"id":"doi:10.1137/s0097539792225935","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539792225935","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100702189","display_name":"Bin Fu","orcid":"https://orcid.org/0000-0001-7192-2983"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Bin Fu","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5101664438","display_name":"Hongzhou Li","orcid":"https://orcid.org/0000-0001-7651-9923"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hong-Zhou Li","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100702189"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.13856988,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"23","issue":"2","first_page":"255","last_page":"260"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9994000196456909,"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/T11567","display_name":"semigroups and automata theory","score":0.9994000196456909,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9977999925613403,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9977999925613403,"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/combinatorics","display_name":"Combinatorics","score":0.8269262313842773},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6545491218566895},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5035762190818787},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.49309584498405457},{"id":"https://openalex.org/keywords/np-complete","display_name":"NP-complete","score":0.4874143898487091},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4325607419013977},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39079320430755615},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11468440294265747}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8269262313842773},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6545491218566895},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5035762190818787},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.49309584498405457},{"id":"https://openalex.org/C122749075","wikidata":"https://www.wikidata.org/wiki/Q215206","display_name":"NP-complete","level":3,"score":0.4874143898487091},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4325607419013977},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39079320430755615},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11468440294265747},{"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":1,"locations":[{"id":"doi:10.1137/s0097539792225935","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539792225935","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1966945335","https://openalex.org/W1971691873","https://openalex.org/W1982849835","https://openalex.org/W1986448430","https://openalex.org/W1989159237","https://openalex.org/W2033323875","https://openalex.org/W2039334189","https://openalex.org/W2044504659","https://openalex.org/W2073777163","https://openalex.org/W2081902982","https://openalex.org/W2402054513"],"related_works":["https://openalex.org/W2062731608","https://openalex.org/W1519201794","https://openalex.org/W4312809402","https://openalex.org/W2606468876","https://openalex.org/W1629505938","https://openalex.org/W2767824041","https://openalex.org/W1547393828","https://openalex.org/W1828234149","https://openalex.org/W2384822215","https://openalex.org/W2082247452"],"abstract_inverted_index":{"Let":[0],"A":[1,12,39,53],"be":[2,7,16,70,82,93,105,121,132],"a":[3,8],"language":[4],"and":[5],"C":[6],"class":[9],"of":[10],"languages.":[11],"is":[13,40,49,54],"said":[14,51],"to":[15],"s-C-close":[17],"(s-C-outside-close)":[18],"if":[19],"there":[20],"exists":[21],"$B":[22],"\\in":[23],"C$":[24],"such":[25],"that":[26,52],"$\\|(A\\Delta":[27],"B)^{":[28],"\\leqslant":[29,32],"n}":[30],"\\|":[31],"s(n)$":[33],"(and":[34],"$A":[35],"\\subseteq":[36,112,138],"B$).":[37],"If":[38],"q-C-close":[41],"(q-C-,outside-close)":[42],"for":[43],"some":[44],"polynomial":[45],"q":[46],"then":[47],"it":[48],"simply":[50],"C-close":[55],"(C-outside-close).":[56],"The":[57],"following":[58],"results":[59],"are":[60],"shown":[61],"in":[62],"this":[63],"paper.":[64],"(1)":[65],"No":[66,78,89,101,117,128],"$NP$-hard":[67,79,90,102,118,129],"set":[68,80,91,103,119,130],"can":[69,81,92,104,120,131],"$coNP$":[71],"-close":[72],"unless":[73,84,96,110,123,136],"$NP":[74,85,97,111,124,137],"=":[75,86,98,108,114,125,134,140],"coNP$.":[76],"(2)":[77],"R-close":[83],"R$.":[87],"(3)":[88],"$O(\\log":[94,106],"n)$-$UP$-close":[95],"{\\textit{Few}}P$.":[99,126],"(4)":[100],"n)$-$C_":[107],"P$-close":[109],"C_":[113,139],"P$.":[115,141],"(5)":[116],"$UP$-outside-close":[122],"(6)":[127],"$C_":[133],"P$-outside-close":[135]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
