{"id":"https://openalex.org/W1980276492","doi":"https://doi.org/10.1145/1132516.1132537","title":"On the solution-space geometry of random constraint satisfaction problems","display_name":"On the solution-space geometry of random constraint satisfaction problems","publication_year":2006,"publication_date":"2006-05-21","ids":{"openalex":"https://openalex.org/W1980276492","doi":"https://doi.org/10.1145/1132516.1132537","mag":"1980276492"},"language":"en","primary_location":{"id":"doi:10.1145/1132516.1132537","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1132516.1132537","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the thirty-eighth annual ACM symposium on Theory of Computing","raw_type":"proceedings-article"},"type":"conference-paper","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/A5021300666","display_name":"Dimitris Achlioptas","orcid":"https://orcid.org/0000-0003-2349-822X"},"institutions":[{"id":"https://openalex.org/I185103710","display_name":"University of California, Santa Cruz","ror":"https://ror.org/03s65by71","country_code":"US","type":"education","lineage":["https://openalex.org/I185103710"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dimitris Achlioptas","raw_affiliation_strings":["University of California Santa Cruz","University of California/Santa Cruz"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California Santa Cruz","institution_ids":["https://openalex.org/I185103710"]},{"raw_affiliation_string":"University of California/Santa Cruz","institution_ids":["https://openalex.org/I185103710"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056141397","display_name":"Federico Ricci\u2010Tersenghi","orcid":"https://orcid.org/0000-0003-4970-7376"},"institutions":[{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Federico Ricci-Tersenghi","raw_affiliation_strings":["University of Rome \"La Sapienza\""],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Rome \"La Sapienza\"","institution_ids":["https://openalex.org/I861853513"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":157,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"130","last_page":"139"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9998999834060669,"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":0.9998999834060669,"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/T11106","display_name":"Data Management and Algorithms","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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":0.9865999817848206,"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/constraint-satisfaction-problem","display_name":"Constraint satisfaction problem","score":0.828644335269928},{"id":"https://openalex.org/keywords/hypergraph","display_name":"Hypergraph","score":0.658187747001648},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.6326383948326111},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.5917879939079285},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5910703539848328},{"id":"https://openalex.org/keywords/constraint-satisfaction-dual-problem","display_name":"Constraint satisfaction dual problem","score":0.5580148696899414},{"id":"https://openalex.org/keywords/constraint-satisfaction","display_name":"Constraint satisfaction","score":0.5328348875045776},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5085254907608032},{"id":"https://openalex.org/keywords/complexity-of-constraint-satisfaction","display_name":"Complexity of constraint satisfaction","score":0.4911775290966034},{"id":"https://openalex.org/keywords/local-consistency","display_name":"Local consistency","score":0.47458529472351074},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.46278315782546997},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4553069472312927},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.4300718605518341},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4193532466888428},{"id":"https://openalex.org/keywords/constraint-graph","display_name":"Constraint graph","score":0.4122988283634186},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3703234791755676},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.35517776012420654},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.31999608874320984}],"concepts":[{"id":"https://openalex.org/C199622910","wikidata":"https://www.wikidata.org/wiki/Q1128326","display_name":"Constraint satisfaction problem","level":3,"score":0.828644335269928},{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.658187747001648},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.6326383948326111},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.5917879939079285},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5910703539848328},{"id":"https://openalex.org/C183046576","wikidata":"https://www.wikidata.org/wiki/Q5164380","display_name":"Constraint satisfaction dual problem","level":5,"score":0.5580148696899414},{"id":"https://openalex.org/C44616089","wikidata":"https://www.wikidata.org/wiki/Q30158686","display_name":"Constraint satisfaction","level":3,"score":0.5328348875045776},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5085254907608032},{"id":"https://openalex.org/C132180345","wikidata":"https://www.wikidata.org/wiki/Q5156628","display_name":"Complexity of constraint satisfaction","level":5,"score":0.4911775290966034},{"id":"https://openalex.org/C137105694","wikidata":"https://www.wikidata.org/wiki/Q3407510","display_name":"Local consistency","level":4,"score":0.47458529472351074},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.46278315782546997},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4553069472312927},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.4300718605518341},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4193532466888428},{"id":"https://openalex.org/C178481205","wikidata":"https://www.wikidata.org/wiki/Q5164372","display_name":"Constraint graph","level":5,"score":0.4122988283634186},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3703234791755676},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35517776012420654},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31999608874320984},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1145/1132516.1132537","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1132516.1132537","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the thirty-eighth annual ACM symposium on Theory of Computing","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.110.9205","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.110.9205","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.gatech.edu/~tetali/MATH8823/AR06.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.219.3001","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.219.3001","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.ucsc.edu/~optas/papers/fp68-achlioptas.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.341.7377","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.341.7377","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/cs/0611052v2.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.342.8261","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.342.8261","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/cs/0611052v1.pdf","raw_type":"text"},{"id":"pmh:oai:iris.uniroma1.it:11573/208196","is_oa":false,"landing_page_url":"http://hdl.handle.net/11573/208196","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"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/conferenceObject"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W24795404","https://openalex.org/W67367170","https://openalex.org/W242035403","https://openalex.org/W1518885151","https://openalex.org/W1537769454","https://openalex.org/W1672032933","https://openalex.org/W1978113428","https://openalex.org/W1978732816","https://openalex.org/W1979720612","https://openalex.org/W1985250014","https://openalex.org/W1996338626","https://openalex.org/W2000931246","https://openalex.org/W2008310023","https://openalex.org/W2010193278","https://openalex.org/W2023622935","https://openalex.org/W2026129786","https://openalex.org/W2051580875","https://openalex.org/W2063428816","https://openalex.org/W2078137578","https://openalex.org/W2081642252","https://openalex.org/W2100020751","https://openalex.org/W2108446739","https://openalex.org/W2115730400","https://openalex.org/W2115885909","https://openalex.org/W2119414881","https://openalex.org/W2138778293","https://openalex.org/W2144919274","https://openalex.org/W2145098470","https://openalex.org/W2149108377","https://openalex.org/W2152182443","https://openalex.org/W2164346692","https://openalex.org/W2168290833"],"related_works":["https://openalex.org/W2784687883","https://openalex.org/W2091348864","https://openalex.org/W2569549435","https://openalex.org/W2737098235","https://openalex.org/W2295056692","https://openalex.org/W2724280655","https://openalex.org/W2012141606","https://openalex.org/W2906226597","https://openalex.org/W4285464797","https://openalex.org/W1551482454"],"abstract_inverted_index":{"For":[0],"a":[1,122,153],"number":[2,86],"of":[3,21,51,59,62,87,90,117,129,145],"random":[4,10,13,168],"constraint":[5,24,169],"satisfaction":[6,170],"problems,":[7],"such":[8,66,118],"as":[9,68],"k-SAT":[11],"and":[12,95],"graph/hypergraph":[14],"coloring,":[15],"there":[16],"are":[17,70,108],"very":[18],"good":[19],"estimates":[20],"the":[22,49,57,60,127,130,137,146],"largest":[23],"density":[25],"for":[26,35,126],"which":[27,91],"solutions":[28,41,63,79],"exist.":[29],"Yet,":[30],"all":[31,99],"known":[32],"polynomial-time":[33,131],"algorithms":[34,132],"these":[36],"problems":[37,67],"fail":[38],"to":[39,163],"find":[40],"even":[42],"at":[43],"much":[44,77],"lower":[45],"densities.":[46],"To":[47],"understand":[48],"origin":[50],"this":[52],"gap":[53],"we":[54,74],"study":[55],"how":[56],"structure":[58],"space":[61],"evolves":[64],"in":[65,158],"constraints":[69],"added.":[71],"In":[72],"particular,":[73],"prove":[75],"that":[76,161],"before":[78],"disappear,":[80],"they":[81],"organize":[82],"into":[83],"an":[84],"exponential":[85],"clusters,":[88],"each":[89,104],"is":[92],"relatively":[93],"small":[94],"far":[96],"apart":[97],"from":[98],"other":[100],"clusters.":[101],"Moreover,":[102],"inside":[103],"cluster":[105],"most":[106],"variables":[107,120],"frozen,":[109],"i.e.,":[110],"take":[111],"only":[112],"one":[113,144],"value.":[114],"The":[115],"existence":[116],"frozen":[119],"gives":[121],"satisfying":[123],"intuitive":[124],"explanation":[125],"failure":[128],"analyzed":[133],"so":[134],"far.":[135],"At":[136],"same":[138],"time,":[139],"our":[140],"results":[141],"establish":[142],"rigorously":[143],"two":[147],"main":[148],"hypotheses":[149],"underlying":[150],"Survey":[151],"Propagation,":[152],"heuristic":[154],"introduced":[155],"by":[156],"physicists":[157],"recent":[159],"years":[160],"appears":[162],"perform":[164],"extraordinarily":[165],"well":[166],"on":[167],"problems.":[171]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":7}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}