{"id":"https://openalex.org/W2034437384","doi":"https://doi.org/10.1145/2629620","title":"Satisfiability Allows No Nontrivial Sparsification unless the Polynomial-Time Hierarchy Collapses","display_name":"Satisfiability Allows No Nontrivial Sparsification unless the Polynomial-Time Hierarchy Collapses","publication_year":2014,"publication_date":"2014-07-01","ids":{"openalex":"https://openalex.org/W2034437384","doi":"https://doi.org/10.1145/2629620","mag":"2034437384"},"language":"en","primary_location":{"id":"doi:10.1145/2629620","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2629620","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","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/A5052689442","display_name":"Holger Dell","orcid":"https://orcid.org/0000-0001-8955-0786"},"institutions":[{"id":"https://openalex.org/I4210094115","display_name":"Laboratoire d'Informatique Algorithmique: Fondements et Applications","ror":"https://ror.org/00pbqgm18","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I4210094115","https://openalex.org/I4210159245"]},{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Holger Dell","raw_affiliation_strings":["LIAFA, Universit\u00e9 Paris Diderot, France"],"affiliations":[{"raw_affiliation_string":"LIAFA, Universit\u00e9 Paris Diderot, France","institution_ids":["https://openalex.org/I4210094115","https://openalex.org/I204730241"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111961315","display_name":"Dieter van Melkebeek","orcid":null},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dieter Van Melkebeek","raw_affiliation_strings":["University of Wisconsin-Madison","University of Wisconsin, Madison"],"affiliations":[{"raw_affiliation_string":"University of Wisconsin-Madison","institution_ids":["https://openalex.org/I135310074"]},{"raw_affiliation_string":"University of Wisconsin, Madison","institution_ids":["https://openalex.org/I135310074"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5052689442"],"corresponding_institution_ids":["https://openalex.org/I204730241","https://openalex.org/I4210094115"],"apc_list":null,"apc_paid":null,"fwci":11.3947,"has_fulltext":false,"cited_by_count":157,"citation_normalized_percentile":{"value":0.98862025,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"61","issue":"4","first_page":"1","last_page":"27"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9998000264167786,"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/T12288","display_name":"Optimization and Search Problems","score":0.9934999942779541,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/kernelization","display_name":"Kernelization","score":0.806880533695221},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7134754657745361},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.712145209312439},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.650046706199646},{"id":"https://openalex.org/keywords/vertex-cover","display_name":"Vertex cover","score":0.6194117069244385},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5538983941078186},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5411950349807739},{"id":"https://openalex.org/keywords/satisfiability","display_name":"Satisfiability","score":0.5399513244628906},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5005624294281006},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.4686296284198761},{"id":"https://openalex.org/keywords/boolean-satisfiability-problem","display_name":"Boolean satisfiability problem","score":0.41855114698410034},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.32183974981307983}],"concepts":[{"id":"https://openalex.org/C207225210","wikidata":"https://www.wikidata.org/wiki/Q1759539","display_name":"Kernelization","level":3,"score":0.806880533695221},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7134754657745361},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.712145209312439},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.650046706199646},{"id":"https://openalex.org/C40687702","wikidata":"https://www.wikidata.org/wiki/Q11515519","display_name":"Vertex cover","level":3,"score":0.6194117069244385},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5538983941078186},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5411950349807739},{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.5399513244628906},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5005624294281006},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4686296284198761},{"id":"https://openalex.org/C6943359","wikidata":"https://www.wikidata.org/wiki/Q875276","display_name":"Boolean satisfiability problem","level":2,"score":0.41855114698410034},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.32183974981307983},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2629620","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2629620","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2481042672","display_name":null,"funder_award_id":"CCF-0728809, CCF-1017597, CCF-1319822","funder_id":"https://openalex.org/F4320337387","funder_display_name":"Division of Computing and Communication Foundations"}],"funders":[{"id":"https://openalex.org/F4320308269","display_name":"Alexander von Humboldt-Stiftung","ror":"https://ror.org/012kf4317"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320337387","display_name":"Division of Computing and Communication Foundations","ror":"https://ror.org/01mng8331"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":65,"referenced_works":["https://openalex.org/W36639738","https://openalex.org/W1517036688","https://openalex.org/W1517585663","https://openalex.org/W1527197079","https://openalex.org/W1540625694","https://openalex.org/W1544829330","https://openalex.org/W1559492868","https://openalex.org/W1570425181","https://openalex.org/W1587602953","https://openalex.org/W1596624097","https://openalex.org/W1821538950","https://openalex.org/W1965645254","https://openalex.org/W1970630090","https://openalex.org/W1973852671","https://openalex.org/W1974810008","https://openalex.org/W1977699786","https://openalex.org/W1979740015","https://openalex.org/W1986602165","https://openalex.org/W1987580556","https://openalex.org/W1995725694","https://openalex.org/W1998552318","https://openalex.org/W1998964055","https://openalex.org/W1999681430","https://openalex.org/W2004181701","https://openalex.org/W2006252547","https://openalex.org/W2006822886","https://openalex.org/W2010193278","https://openalex.org/W2012931553","https://openalex.org/W2016341899","https://openalex.org/W2023600080","https://openalex.org/W2033152671","https://openalex.org/W2036265926","https://openalex.org/W2038073775","https://openalex.org/W2038691311","https://openalex.org/W2051784313","https://openalex.org/W2061881283","https://openalex.org/W2069139349","https://openalex.org/W2075577372","https://openalex.org/W2079401865","https://openalex.org/W2083748805","https://openalex.org/W2087964954","https://openalex.org/W2088419249","https://openalex.org/W2091434162","https://openalex.org/W2107284348","https://openalex.org/W2115334306","https://openalex.org/W2116887008","https://openalex.org/W2118728198","https://openalex.org/W2125455032","https://openalex.org/W2144475416","https://openalex.org/W2145098470","https://openalex.org/W2152351539","https://openalex.org/W2159892713","https://openalex.org/W2161620758","https://openalex.org/W2170055332","https://openalex.org/W2400994770","https://openalex.org/W2401610261","https://openalex.org/W2405367548","https://openalex.org/W2913688336","https://openalex.org/W3008660429","https://openalex.org/W3030488835","https://openalex.org/W3098466722","https://openalex.org/W4292230561","https://openalex.org/W4298227433","https://openalex.org/W4389615664","https://openalex.org/W6630973240"],"related_works":["https://openalex.org/W2381408042","https://openalex.org/W2425261484","https://openalex.org/W33845589","https://openalex.org/W189387296","https://openalex.org/W4388276051","https://openalex.org/W2161286454","https://openalex.org/W2964273883","https://openalex.org/W2886237949","https://openalex.org/W2355184605","https://openalex.org/W2122202324"],"abstract_inverted_index":{"Consider":[0],"the":[1,16,24,54,58,65,69,113,126,145,188,250,253,270],"following":[2],"two-player":[3],"communication":[4,63],"process":[5],"to":[6,42,48,68,117],"decide":[7,43],"a":[8,95,137,221],"language":[9],"L":[10,49],":":[11],"The":[12,121,207],"first":[13,66,127],"player":[14,26,67,128],"holds":[15,124,200],"entire":[17],"input":[18],"x":[19,37,46],"but":[20,30],"is":[21,27,41,57,107,129,132,149,225,244],"polynomially":[22],"bounded;":[23],"second":[25,70],"computationally":[28],"unbounded":[29],"does":[31],"not":[32,150],"know":[33],"any":[34,73,202],"part":[35],"of":[36,60,62,97,161,233,252,258],";":[38],"their":[39],"goal":[40],"cooperatively":[44],"whether":[45],"belongs":[47],"at":[50],"small":[51],"cost,":[52],"where":[53,247],"cost":[55,98],"measure":[56],"number":[59],"bits":[61],"from":[64],"player.":[71],"For":[72,187],"integer":[74,203],"d":[75,91,195,204,209],"\u2265":[76,205],"3":[77],"and":[78,131,174,278],"positive":[79],"real":[80],"\u03b5":[81,103,141,239],",":[82],"we":[83],"show":[84],"that,":[85],"if":[86],"satisfiability":[87],"for":[88,140,159,183,201,266],"n":[89,193],"-variable":[90],"-CNF":[92],"formulas":[93],"has":[94],"protocol":[96,139],"O":[99,234,259],"(":[100,235,260],"nd":[101],"\u2212":[102,238],"),":[104],"then":[105],"coNP":[106,148,243],"in":[108,151,163,169,245,269],"NP/poly,":[109,152,246],"which":[110],"implies":[111,155,212],"that":[112,147,213,224],"polynomial-time":[114],"hierarchy":[115],"collapses":[116],"its":[118],"third":[119],"level.":[120],"result":[122,154],"even":[123],"when":[125],"conondeterministic,":[130],"tight":[133,156],"as":[134],"there":[135],"exists":[136],"trivial":[138],"=":[142,210],"0.":[143],"Under":[144],"hypothesis":[146],"our":[153],"lower":[157],"bounds":[158],"parameters":[160],"interest":[162],"several":[164,267],"areas,":[165],"namely":[166],"sparsification,":[167],"kernelization":[168],"parameterized":[170],"complexity,":[171],"lossy":[172],"compression,":[173],"probabilistically":[175],"checkable":[176],"proofs.":[177],"By":[178],"reduction,":[179],"similar":[180],"results":[181],"hold":[182],"other":[184],"NP-complete":[185],"problems.":[186],"vertex":[189,216,273,276],"cover":[190],"problem":[191,218],"on":[192,220],"-vertex":[194],"-uniform":[196],"hypergraphs,":[197],"this":[198],"statement":[199],"2.":[206],"case":[208],"2":[211,237],"no":[214],"NP-hard":[215],"deletion":[217,254],"based":[219],"graph":[222],"property":[223],"inherited":[226],"by":[227],"subgraphs":[228],"can":[229],"have":[230],"kernels":[231],"consisting":[232,257],"k":[236,248,261],")":[240],"edges":[241,263],"unless":[242],"denotes":[249],"size":[251],"set.":[255],"Kernels":[256],"2)":[262],"are":[264],"known":[265],"problems":[268],"class,":[271],"including":[272],"cover,":[274],"feedback":[275],"set,":[277],"bounded-degree":[279],"deletion.":[280]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":16},{"year":2019,"cited_by_count":14},{"year":2018,"cited_by_count":47},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":11},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
