{"id":"https://openalex.org/W2133747498","doi":"https://doi.org/10.1017/s0963548303005637","title":"Some Results on Random Unsatisfiable <i>k</i>-Sat Instances and Approximation Algorithms Applied to Random Structures","display_name":"Some Results on Random Unsatisfiable <i>k</i>-Sat Instances and Approximation Algorithms Applied to Random Structures","publication_year":2003,"publication_date":"2003-05-01","ids":{"openalex":"https://openalex.org/W2133747498","doi":"https://doi.org/10.1017/s0963548303005637","mag":"2133747498"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548303005637","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548303005637","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and 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/A5044686377","display_name":"Andreas Goerdt","orcid":null},"institutions":[{"id":"https://openalex.org/I2610724","display_name":"Chemnitz University of Technology","ror":"https://ror.org/00a208s56","country_code":"DE","type":"education","lineage":["https://openalex.org/I2610724"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"ANDREAS GOERDT","raw_affiliation_strings":["Technische Universit\u00e4t Chemnitz, Fakult\u00e4t f\u00fcr Informatik, Stra\u00dfe der Nationen 62, 09107 Chemnitz, Germany (e-mail:","Technische Universit\u00e4t Chemnitz, Fakult\u00e4t f\u00fcr Informatik, Stra\u00dfe der Nationen 62, 09107 Chemnitz, Germany (e-mail: goerdt@informatik.tu-chemnitz.de)#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technische Universit\u00e4t Chemnitz, Fakult\u00e4t f\u00fcr Informatik, Stra\u00dfe der Nationen 62, 09107 Chemnitz, Germany (e-mail:","institution_ids":["https://openalex.org/I2610724"]},{"raw_affiliation_string":"Technische Universit\u00e4t Chemnitz, Fakult\u00e4t f\u00fcr Informatik, Stra\u00dfe der Nationen 62, 09107 Chemnitz, Germany (e-mail: goerdt@informatik.tu-chemnitz.de)#TAB#","institution_ids":["https://openalex.org/I2610724"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110229796","display_name":"TOMASZ JURDZISKI","orcid":null},"institutions":[{"id":"https://openalex.org/I11923345","display_name":"Wroc\u0142aw University of Science and Technology","ror":"https://ror.org/008fyn775","country_code":"PL","type":"education","lineage":["https://openalex.org/I11923345"]},{"id":"https://openalex.org/I219388962","display_name":"University of Wroc\u0142aw","ror":"https://ror.org/00yae6e25","country_code":"PL","type":"education","lineage":["https://openalex.org/I219388962"]},{"id":"https://openalex.org/I4210087266","display_name":"Institute of Computer Science","ror":"https://ror.org/003fvp964","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210087266","https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"TOMASZ JURDZI\u0143SKI","raw_affiliation_strings":["Wroclaw University, Institute of Computer Science, Przesmyckiego 20, 50-151 Wroclaw, Poland (e-mail:","Wroclaw University, Institute of Computer Science, Przesmyckiego 20, 50-151 Wroclaw, Poland (e-mail: tju@ii.uni.wroc.pl)#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Wroclaw University, Institute of Computer Science, Przesmyckiego 20, 50-151 Wroclaw, Poland (e-mail:","institution_ids":["https://openalex.org/I219388962","https://openalex.org/I11923345"]},{"raw_affiliation_string":"Wroclaw University, Institute of Computer Science, Przesmyckiego 20, 50-151 Wroclaw, Poland (e-mail: tju@ii.uni.wroc.pl)#TAB#","institution_ids":["https://openalex.org/I219388962","https://openalex.org/I4210087266"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5044686377"],"corresponding_institution_ids":["https://openalex.org/I2610724"],"apc_list":null,"apc_paid":null,"fwci":4.0036,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.94208391,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"12","issue":"3","first_page":"245","last_page":"267"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9991000294685364,"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":0.9991000294685364,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9857000112533569,"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"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9851999878883362,"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/satisfiability","display_name":"Satisfiability","score":0.7515075206756592},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.6340497732162476},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5971970558166504},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5966429114341736},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.5103873610496521},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.49680307507514954},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.49643784761428833},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.43722760677337646}],"concepts":[{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.7515075206756592},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.6340497732162476},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5971970558166504},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5966429114341736},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.5103873610496521},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49680307507514954},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.49643784761428833},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.43722760677337646},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.0},{"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:10.1017/s0963548303005637","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548303005637","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W331370188","https://openalex.org/W1491700082","https://openalex.org/W1514925232","https://openalex.org/W1578099820","https://openalex.org/W1601503375","https://openalex.org/W1968864043","https://openalex.org/W1979110822","https://openalex.org/W1999032440","https://openalex.org/W2001508095","https://openalex.org/W2007968698","https://openalex.org/W2018025029","https://openalex.org/W2026634792","https://openalex.org/W2034204728","https://openalex.org/W2043506441","https://openalex.org/W2068871408","https://openalex.org/W2072802070","https://openalex.org/W2401610261","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2306553012","https://openalex.org/W4251417359","https://openalex.org/W4229993731","https://openalex.org/W2381059884","https://openalex.org/W2372756075","https://openalex.org/W1979193983","https://openalex.org/W3037419933","https://openalex.org/W44982509","https://openalex.org/W2952234674","https://openalex.org/W1543051890"],"abstract_inverted_index":{"It":[0],"is":[1,25,72,95],"known":[2,74],"that":[3,30,75,125],"random":[4,16,66,76,126,156],"$k$":[5,84],"-Sat":[6,144],"instances":[7],"with":[8,20,56,78,83,128,158],"at":[9],"least":[10],"$(2^k":[11],"\\cdot":[12,80],"\\ln":[13],"2)\\cdot":[14],"n$":[15],"clauses":[17,82,133],"are":[18,115],"unsatisfiable":[19,139],"high":[21],"probability.":[22],"This":[23,49],"result":[24,97,148],"simply":[26],"obtained":[27],"by":[28,168],"showing":[29],"the":[31,41,61,96,141,151],"expected":[32],"number":[33,42,131,161],"of":[34,43,63,98,132,155,162,171],"satisfying":[35],"assignments":[36],"tends":[37,46],"to":[38,47,100],"$0$":[39],"when":[40],"variables":[44],"$n$":[45],"infinity.":[48],"proof":[50],"does":[51],"not":[52],"directly":[53],"provide":[54],"us":[55],"an":[57],"efficient":[58,69],"algorithm":[59],"certifying":[60],"unsatisfiability":[62],"a":[64,129,159],"given":[65],"formula.":[67],"Concerning":[68],"algorithms,":[70],"it":[71],"essentially":[73],"formulas":[77,127],"$n^\\varepsilon":[79],"n^{k/2}$":[81],"literals":[85],"can":[86,134],"be":[87,135],"efficiently":[88,136],"certified":[89,137],"as":[90,138],"unsatisfiable.":[91],"The":[92],"present":[93],"paper":[94],"trying":[99],"lower":[101],"this":[102],"bound.":[103],"We":[104,164],"obtain":[105,165],"better":[106],"bounds":[107],"for":[108,120,150],"some":[109],"specialized":[110],"satisfiability":[111],"problems.":[112],"These":[113],"results":[114,167],"based":[116],"on":[117],"discrepancy":[118],"investigations":[119],"hypergraphs.":[121],"Further,":[122],"we":[123],"show":[124],"linear":[130,160],"in":[140],"Not-All-Equal-":[142],"$3$":[143,153],"sense.":[145],"A":[146],"similar":[147],"holds":[149],"non-":[152],"-colourability":[154],"graphs":[157],"edges.":[163],"these":[166],"direct":[169],"application":[170],"approximation":[172],"algorithms.":[173]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2016-06-24T00:00:00"}
