{"id":"https://openalex.org/W67367170","doi":"https://doi.org/10.1103/physreve.66.056126","title":"Random K -satisfiability problem: From an analytic solution to an efficient algorithm","display_name":"Random K -satisfiability problem: From an analytic solution to an efficient algorithm","publication_year":2002,"publication_date":"2002-11-26","ids":{"openalex":"https://openalex.org/W67367170","doi":"https://doi.org/10.1103/physreve.66.056126","mag":"67367170","pmid":"https://pubmed.ncbi.nlm.nih.gov/12513575"},"language":"en","primary_location":{"id":"doi:10.1103/physreve.66.056126","doi":"https://doi.org/10.1103/physreve.66.056126","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physreve.66.056126","pdf_url":null,"source":{"id":"https://openalex.org/S4210224030","display_name":"Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics","issn_l":"1063-651X","issn":["1063-651X","1095-3787","1538-4519"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review E","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/cond-mat/0207194","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037000437","display_name":"Marc M\u00e9zard","orcid":"https://orcid.org/0000-0003-4591-3893","observed_orcids":["https://orcid.org/0000-0003-4591-3893"]},"institutions":[{"id":"https://openalex.org/I102197404","display_name":"Universit\u00e9 Paris-Sud","ror":"https://ror.org/028rypz17","country_code":"FR","type":"education","lineage":["https://openalex.org/I102197404","https://openalex.org/I277688954"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210097733","display_name":"Laboratoire de Physique Th\u00e9orique et Mod\u00e8les Statistiques","ror":"https://ror.org/00w67e447","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I4210097733"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Marc M\u00e9zard","raw_affiliation_strings":["Laboratoire de Physique Th\u00e9orique et Mod\u00e8les Statistiques, CNRS and Universit\u00e9 Paris Sud, B\u00e2timent 100, 91405 Orsay Cedex, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire de Physique Th\u00e9orique et Mod\u00e8les Statistiques, CNRS and Universit\u00e9 Paris Sud, B\u00e2timent 100, 91405 Orsay Cedex, France","institution_ids":["https://openalex.org/I102197404","https://openalex.org/I1294671590","https://openalex.org/I4210097733"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041685522","display_name":"Riccardo Zecchina","orcid":"https://orcid.org/0000-0002-1221-5207","observed_orcids":["https://orcid.org/0000-0002-1221-5207"]},"institutions":[{"id":"https://openalex.org/I12323705","display_name":"The Abdus Salam International Centre for Theoretical Physics (ICTP)","ror":"https://ror.org/009gyvm78","country_code":"IT","type":"facility","lineage":["https://openalex.org/I12323705","https://openalex.org/I1286959531","https://openalex.org/I1293226324","https://openalex.org/I2801247003"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Riccardo Zecchina","raw_affiliation_strings":["The Abdus Salam International Centre for Theoretical Physics, Statistical Mechanics and Interdisciplinary Applications Group, Strada Costiera 11, 34100 Trieste, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Abdus Salam International Centre for Theoretical Physics, Statistical Mechanics and Interdisciplinary Applications Group, Strada Costiera 11, 34100 Trieste, Italy","institution_ids":["https://openalex.org/I12323705"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":31.5399,"has_fulltext":false,"cited_by_count":448,"citation_normalized_percentile":{"value":0.99564101,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"66","issue":"5","first_page":"056126","last_page":"056126"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9775000214576721,"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"}},"topics":[{"id":"https://openalex.org/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9775000214576721,"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/T10591","display_name":"Theoretical and Computational Physics","score":0.01549999974668026,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.0006000000284984708,"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/3-sat","display_name":"3-SAT","score":0.7429999709129333},{"id":"https://openalex.org/keywords/cavity-method","display_name":"cavity method","score":0.8539999723434448},{"id":"https://openalex.org/keywords/zero-temperature","display_name":"zero temperature","score":0.7059999704360962},{"id":"https://openalex.org/keywords/phase-diagram","display_name":"phase diagram","score":0.9340000152587891},{"id":"https://openalex.org/keywords/metastable-states","display_name":"metastable states","score":0.9900000095367432},{"id":"https://openalex.org/keywords/order-parameter","display_name":"order parameter","score":0.7419999837875366},{"id":"https://openalex.org/keywords/combinatorial-optimization-algorithms","display_name":"combinatorial optimization algorithms","score":0.7620000243186951},{"id":"https://openalex.org/keywords/satisfiability","display_name":"satisfiability","score":0.39800000190734863}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.7123955488204956},{"id":"https://openalex.org/C89464430","wikidata":"https://www.wikidata.org/wiki/Q849516","display_name":"Metastability","level":2,"score":0.538265585899353},{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.5201980471611023},{"id":"https://openalex.org/C6943359","wikidata":"https://www.wikidata.org/wiki/Q875276","display_name":"Boolean satisfiability problem","level":2,"score":0.5193173289299011},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.490102618932724},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.45881280303001404},{"id":"https://openalex.org/C111797529","wikidata":"https://www.wikidata.org/wiki/Q17080584","display_name":"Maximum satisfiability problem","level":3,"score":0.4470250904560089},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.42866218090057373},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3282719850540161},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14849895238876343},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.14627626538276672},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09480553865432739},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1103/physreve.66.056126","doi":"https://doi.org/10.1103/physreve.66.056126","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physreve.66.056126","pdf_url":null,"source":{"id":"https://openalex.org/S4210224030","display_name":"Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics","issn_l":"1063-651X","issn":["1063-651X","1095-3787","1538-4519"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review E","raw_type":"journal-article"},{"id":"pmid:12513575","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/12513575","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical review. E, Statistical, nonlinear, and soft matter physics","raw_type":"Journal Article"},{"id":"pmh:oai:arXiv.org:cond-mat/0207194","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/cond-mat/0207194","pdf_url":"https://arxiv.org/pdf/cond-mat/0207194","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-00002362v1","doi":null,"is_oa":false,"landing_page_url":"https://hal.science/hal-00002362","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Physical Review E : Statistical, Nonlinear, and Soft Matter Physics [2001-2015], 2002, 66, pp.056126","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:iris.polito.it:11583/1829471","doi":null,"is_oa":false,"landing_page_url":"http://hdl.handle.net/11583/1829471","pdf_url":null,"source":{"id":"https://openalex.org/S7407055329","display_name":"PORTO@Iris","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.cond-mat/0207194","doi":"https://doi.org/10.48550/arxiv.cond-mat/0207194","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.cond-mat/0207194","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:cond-mat/0207194","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/cond-mat/0207194","pdf_url":"https://arxiv.org/pdf/cond-mat/0207194","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":49,"referenced_works":["https://openalex.org/W242035403","https://openalex.org/W1504317671","https://openalex.org/W1508206977","https://openalex.org/W1510651616","https://openalex.org/W1517461401","https://openalex.org/W1518885151","https://openalex.org/W1532831879","https://openalex.org/W1534832769","https://openalex.org/W1633549751","https://openalex.org/W1650993530","https://openalex.org/W1772716870","https://openalex.org/W1963913579","https://openalex.org/W1965121855","https://openalex.org/W1968198053","https://openalex.org/W1973670813","https://openalex.org/W1984178196","https://openalex.org/W2002651865","https://openalex.org/W2006424894","https://openalex.org/W2007995670","https://openalex.org/W2011039300","https://openalex.org/W2019599312","https://openalex.org/W2022083710","https://openalex.org/W2023360441","https://openalex.org/W2024060531","https://openalex.org/W2032781595","https://openalex.org/W2036265926","https://openalex.org/W2042162837","https://openalex.org/W2049204972","https://openalex.org/W2055340828","https://openalex.org/W2063102449","https://openalex.org/W2089435411","https://openalex.org/W2098678088","https://openalex.org/W2100008268","https://openalex.org/W2107993699","https://openalex.org/W2125490292","https://openalex.org/W2137813581","https://openalex.org/W2138778293","https://openalex.org/W2154061444","https://openalex.org/W2155218845","https://openalex.org/W2158907280","https://openalex.org/W2173249896","https://openalex.org/W2404266688","https://openalex.org/W2949727674","https://openalex.org/W2951682774","https://openalex.org/W2990332611","https://openalex.org/W3143264742","https://openalex.org/W4213009134","https://openalex.org/W4240147683","https://openalex.org/W4293879729"],"related_works":["https://openalex.org/W2408080066","https://openalex.org/W2394616262","https://openalex.org/W192406999","https://openalex.org/W2406837904","https://openalex.org/W3152212242","https://openalex.org/W2014111643","https://openalex.org/W2102364390","https://openalex.org/W1913543287","https://openalex.org/W2336941104","https://openalex.org/W2571882453"],"abstract_inverted_index":{"We":[0,31],"study":[1],"the":[2,16,24,28,33,40,44,51,54,65,77,82,115],"problem":[3],"of":[4,6,35,46,53,56,70,72,81,100],"satisfiability":[5,117],"randomly":[7],"chosen":[8],"clauses,":[9],"each":[10],"with":[11,119],"K":[12],"Boolean":[13],"variables.":[14],"Using":[15],"cavity":[17,66],"method":[18],"at":[19,50],"zero":[20],"temperature,":[21],"we":[22],"find":[23],"phase":[25,38],"diagram":[26],"for":[27,87,102,114],"K=3":[29,116],"case.":[30],"show":[32],"existence":[34],"an":[36],"intermediate":[37],"in":[39,64,76],"satisfiable":[41],"region,":[42],"where":[43],"proliferation":[45],"metastable":[47],"states":[48,80],"is":[49,111],"origin":[52],"slowdown":[55],"search":[57],"algorithms.":[58],"The":[59],"fundamental":[60],"order":[61],"parameter":[62],"introduced":[63],"method,":[67],"which":[68],"consists":[69],"surveys":[71,92],"local":[73],"magnetic":[74],"fields":[75],"various":[78],"possible":[79],"system,":[83],"can":[84,93],"be":[85,94],"computed":[86],"one":[88],"given":[89],"sample.":[90],"These":[91],"used":[95],"to":[96],"invent":[97],"new":[98],"types":[99],"algorithms":[101],"solving":[103],"hard":[104],"combinatorial":[105],"optimizations":[106],"problems.":[107],"One":[108],"such":[109],"algorithm":[110],"shown":[112],"here":[113],"problem,":[118],"very":[120],"good":[121],"performances.":[122]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":12},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":11},{"year":2015,"cited_by_count":13},{"year":2014,"cited_by_count":11},{"year":2013,"cited_by_count":21},{"year":2012,"cited_by_count":16}],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2016-06-24T00:00:00"}