{"id":"https://openalex.org/W2061352247","doi":"https://doi.org/10.1137/060673886","title":"Splitting NP-Complete Sets","display_name":"Splitting NP-Complete Sets","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2061352247","doi":"https://doi.org/10.1137/060673886","mag":"2061352247"},"language":"en","primary_location":{"id":"doi:10.1137/060673886","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060673886","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/A5111915074","display_name":"Christian Gla\u00dfer","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Christian Gla\u00dfer","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112023986","display_name":"A. Pavan","orcid":"https://orcid.org/0000-0003-1665-5266"},"institutions":[{"id":"https://openalex.org/I25974101","display_name":"University of W\u00fcrzburg","ror":"https://ror.org/00fbnyb24","country_code":"DE","type":"education","lineage":["https://openalex.org/I25974101"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"A. Pavan","raw_affiliation_strings":["University of W\u00fcrzburg"],"affiliations":[{"raw_affiliation_string":"University of W\u00fcrzburg","institution_ids":["https://openalex.org/I25974101"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051370311","display_name":"Alan L. Selman","orcid":null},"institutions":[{"id":"https://openalex.org/I25974101","display_name":"University of W\u00fcrzburg","ror":"https://ror.org/00fbnyb24","country_code":"DE","type":"education","lineage":["https://openalex.org/I25974101"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Alan L. Selman","raw_affiliation_strings":["University of W\u00fcrzburg"],"affiliations":[{"raw_affiliation_string":"University of W\u00fcrzburg","institution_ids":["https://openalex.org/I25974101"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017478631","display_name":"Liyu Zhang","orcid":"https://orcid.org/0000-0002-6141-3154"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liyu Zhang","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5111915074"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4149,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.63897618,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"37","issue":"5","first_page":"1517","last_page":"1535"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.998199999332428,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9973000288009644,"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":0.7827870845794678},{"id":"https://openalex.org/keywords/pspace","display_name":"PSPACE","score":0.5999985933303833},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5917801260948181},{"id":"https://openalex.org/keywords/turing-machine","display_name":"Turing machine","score":0.5792467594146729},{"id":"https://openalex.org/keywords/complexity-class","display_name":"Complexity class","score":0.5369946956634521},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5142518877983093},{"id":"https://openalex.org/keywords/polynomial-hierarchy","display_name":"Polynomial hierarchy","score":0.49563920497894287},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4724422097206116},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.44489094614982605},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.41110119223594666},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.34531891345977783},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.08118996024131775},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.06744822859764099}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7827870845794678},{"id":"https://openalex.org/C197685441","wikidata":"https://www.wikidata.org/wiki/Q500716","display_name":"PSPACE","level":3,"score":0.5999985933303833},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5917801260948181},{"id":"https://openalex.org/C29248071","wikidata":"https://www.wikidata.org/wiki/Q163310","display_name":"Turing machine","level":3,"score":0.5792467594146729},{"id":"https://openalex.org/C39637292","wikidata":"https://www.wikidata.org/wiki/Q908207","display_name":"Complexity class","level":3,"score":0.5369946956634521},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5142518877983093},{"id":"https://openalex.org/C2776013622","wikidata":"https://www.wikidata.org/wiki/Q2103021","display_name":"Polynomial hierarchy","level":3,"score":0.49563920497894287},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4724422097206116},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.44489094614982605},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.41110119223594666},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.34531891345977783},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.08118996024131775},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.06744822859764099},{"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:10.1137/060673886","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060673886","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:scholarworks.utrgv.edu:cs_fac-1147","is_oa":false,"landing_page_url":"https://scholarworks.utrgv.edu/cs_fac/148","pdf_url":null,"source":{"id":"https://openalex.org/S4306402611","display_name":"ScholarWorks @ UTRGV (The University of Texas Rio Grande Valley)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2802326326","host_organization_name":"The University of Texas Rio Grande Valley","host_organization_lineage":["https://openalex.org/I2802326326"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Computer Science Faculty Publications and Presentations","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.398.6165","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.398.6165","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.iastate.edu/~pavan/papers/split.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1490686376","https://openalex.org/W1497509478","https://openalex.org/W1971070826","https://openalex.org/W1975715978","https://openalex.org/W1978196595","https://openalex.org/W2023336906","https://openalex.org/W2025420511","https://openalex.org/W2030692444","https://openalex.org/W2039334189","https://openalex.org/W2050457719","https://openalex.org/W2067661972","https://openalex.org/W2090186532","https://openalex.org/W2101632555","https://openalex.org/W2106436148","https://openalex.org/W2138494505","https://openalex.org/W2161631645","https://openalex.org/W2169625092"],"related_works":["https://openalex.org/W2085484366","https://openalex.org/W1486286946","https://openalex.org/W2146459129","https://openalex.org/W2950065312","https://openalex.org/W4302414675","https://openalex.org/W278676640","https://openalex.org/W2122747219","https://openalex.org/W2002385864","https://openalex.org/W2082636129","https://openalex.org/W2075449032"],"abstract_inverted_index":{"We":[0,115],"show":[1],"that":[2,90,96,138],"a":[3,16,21,25,94,133],"set":[4,105,135],"is":[5,12,139],"m-autoreducible":[6],"if":[7,10],"and":[8,31,53,63,76,113,121,129,164],"only":[9],"it":[11],"m-mitotic.":[13],"This":[14],"solves":[15,158],"long-standing":[17],"open":[18,84,160],"question":[19,161],"in":[20,136],"surprising":[22],"way.":[23],"As":[24],"consequence":[26],"of":[27,42,60,72],"this":[28,78],"unconditional":[29],"result":[30],"recent":[32],"work":[33],"by":[34,162],"Gla\u00dfer":[35],"et":[36],"al.,":[37],"complete":[38,91],"sets":[39,92,111],"for":[40,123],"all":[41,58,124],"the":[43,64,70,117],"following":[44],"complexity":[45],"classes":[46],"are":[47],"m-mitotic:":[48],"$\\mathrm{NP}$,":[49,73],"$\\mathrm{coNP}$,":[50],"$\\oplus\\mathrm{P}$,":[51],"$\\mathrm{PSPACE}$,":[52,74],"$\\mathrm{NEXP}$,":[54,75],"as":[55,57],"well":[56],"levels":[59],"$\\mathrm{PH}$,":[61,77],"$\\mathrm{MODPH}$,":[62],"Boolean":[65],"hierarchy":[66],"over":[67],"$\\mathrm{NP}$.":[68],"In":[69,101,147],"cases":[71],"at":[79],"once":[80],"answers":[81],"several":[82],"well-studied":[83],"questions.":[85],"These":[86],"results":[87],"tell":[88],"us":[89],"share":[93],"redundancy":[95],"was":[97],"not":[98,143,152],"known":[99],"before.":[100],"particular,":[102,148],"every":[103],"$\\mathrm{NP}$-complete":[104,110],"A":[106],"splits":[107],"into":[108],"two":[109],"$A_1$":[112],"$A_2$.":[114],"disprove":[116],"equivalence":[118],"between":[119,127],"autoreducibility":[120],"mitoticity":[122],"polynomial-time-bounded":[125],"reducibilities":[126],"3-tt-reducibility":[128],"Turing-reducibility:":[130],"There":[131],"exists":[132],"sparse":[134],"$\\mathrm{EXP}$":[137],"polynomial-time":[140,145,149,154],"3-tt-autoreducible,":[141],"but":[142],"weakly":[144],"T-mitotic.":[146],"T-autoreducibility":[150],"does":[151],"imply":[153],"weak":[155],"T-mitoticity,":[156],"which":[157],"an":[159],"Buhrman":[163],"Torenvliet.":[165]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}