{"id":"https://openalex.org/W2045417786","doi":"https://doi.org/10.1137/110832240","title":"A Dichotomy Theorem for the Resolution Complexity of Random Constraint Satisfaction Problems","display_name":"A Dichotomy Theorem for the Resolution Complexity of Random Constraint Satisfaction Problems","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2045417786","doi":"https://doi.org/10.1137/110832240","mag":"2045417786"},"language":"en","primary_location":{"id":"doi:10.1137/110832240","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110832240","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/A5100856892","display_name":"Siu On Chan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Siu On Chan","raw_affiliation_strings":["Department of Computer Science University of Toronto"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science University of Toronto","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072889645","display_name":"Michael Molloy","orcid":"https://orcid.org/0000-0001-5435-1015"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Michael Molloy","raw_affiliation_strings":["Department of Computer Science University of Toronto"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science University of Toronto","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5072889645"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.131,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.81147918,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"42","issue":"1","first_page":"27","last_page":"60"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9976000189781189,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.993399977684021,"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":0.8299727439880371},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7543734312057495},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.623545229434967},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.5698521733283997},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5313782095909119},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.5235171914100647},{"id":"https://openalex.org/keywords/constraint-satisfaction","display_name":"Constraint satisfaction","score":0.500709056854248},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.499713659286499},{"id":"https://openalex.org/keywords/complexity-of-constraint-satisfaction","display_name":"Complexity of constraint satisfaction","score":0.4797426462173462},{"id":"https://openalex.org/keywords/constraint-graph","display_name":"Constraint graph","score":0.4565143585205078},{"id":"https://openalex.org/keywords/resolution","display_name":"Resolution (logic)","score":0.45378515124320984},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4434429705142975},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.44016680121421814},{"id":"https://openalex.org/keywords/constraint-satisfaction-dual-problem","display_name":"Constraint satisfaction dual problem","score":0.4295361638069153},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4188944697380066},{"id":"https://openalex.org/keywords/local-consistency","display_name":"Local consistency","score":0.31031566858291626},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19800391793251038},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15240365266799927},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09195172786712646},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.06362321972846985}],"concepts":[{"id":"https://openalex.org/C199622910","wikidata":"https://www.wikidata.org/wiki/Q1128326","display_name":"Constraint satisfaction problem","level":3,"score":0.8299727439880371},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7543734312057495},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.623545229434967},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.5698521733283997},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5313782095909119},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.5235171914100647},{"id":"https://openalex.org/C44616089","wikidata":"https://www.wikidata.org/wiki/Q30158686","display_name":"Constraint satisfaction","level":3,"score":0.500709056854248},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.499713659286499},{"id":"https://openalex.org/C132180345","wikidata":"https://www.wikidata.org/wiki/Q5156628","display_name":"Complexity of constraint satisfaction","level":5,"score":0.4797426462173462},{"id":"https://openalex.org/C178481205","wikidata":"https://www.wikidata.org/wiki/Q5164372","display_name":"Constraint graph","level":5,"score":0.4565143585205078},{"id":"https://openalex.org/C138268822","wikidata":"https://www.wikidata.org/wiki/Q1051925","display_name":"Resolution (logic)","level":2,"score":0.45378515124320984},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4434429705142975},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.44016680121421814},{"id":"https://openalex.org/C183046576","wikidata":"https://www.wikidata.org/wiki/Q5164380","display_name":"Constraint satisfaction dual problem","level":5,"score":0.4295361638069153},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4188944697380066},{"id":"https://openalex.org/C137105694","wikidata":"https://www.wikidata.org/wiki/Q3407510","display_name":"Local consistency","level":4,"score":0.31031566858291626},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19800391793251038},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15240365266799927},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09195172786712646},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.06362321972846985},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/110832240","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110832240","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:CiteSeerX.psu:10.1.1.219.3470","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.219.3470","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.toronto.edu/~molloy/webpapers/cspfocs.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.644.1008","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.644.1008","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.toronto.edu/~molloy/webpapers/csp11-2.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1533562602","https://openalex.org/W1999678910","https://openalex.org/W2013181989","https://openalex.org/W2015209718","https://openalex.org/W2018277172","https://openalex.org/W2025593265","https://openalex.org/W2033086906","https://openalex.org/W2044722214","https://openalex.org/W2062671967","https://openalex.org/W2071706116","https://openalex.org/W2084384424","https://openalex.org/W2085826829","https://openalex.org/W2088419249","https://openalex.org/W2104427163","https://openalex.org/W2109767783","https://openalex.org/W2126420408","https://openalex.org/W2144512014","https://openalex.org/W2147012241","https://openalex.org/W4301417336"],"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/W2012141606","https://openalex.org/W2906226597","https://openalex.org/W4285464797","https://openalex.org/W1551482454","https://openalex.org/W2922482437"],"abstract_inverted_index":{"We":[0,42,70],"consider":[1],"random":[2,103],"instances":[3],"of":[4,33,74,92],"constraint":[5,17,86],"satisfaction":[6],"problems":[7],"(CSPs)":[8],"where":[9,37],"each":[10,16,75],"variable":[11],"has":[12],"domain":[13],"size":[14],"$O(1)$,":[15],"is":[18,35,39,53,63],"on":[19,85],"$O(1)$":[20],"variables,":[21],"and":[22],"the":[23,50,72,90,102],"constraints":[24,34,94],"are":[25],"chosen":[26],"from":[27],"a":[28,40,82],"specified":[29],"distribution.":[30],"The":[31],"number":[32],"$cn$,":[36],"$c$":[38],"constant.":[41],"prove":[43],"that":[44],"for":[45,57,67],"every":[46,68],"possible":[47],"distribution,":[48],"either":[49],"resolution":[51],"complexity":[52],"almost":[54,64],"surely":[55,65],"polylogarithmic":[56],"sufficiently":[58],"large":[59],"$c$,":[60],"or":[61],"it":[62],"exponential":[66],"$c>0$.":[69],"characterize":[71],"distributions":[73],"type.":[76],"To":[77],"do":[78],"so,":[79],"we":[80],"introduce":[81],"closure":[83],"operation":[84],"sets":[87],"which":[88],"yields":[89],"set":[91],"all":[93],"that,":[95],"in":[96,101],"some":[97],"sense,":[98],"appear":[99],"implicitly":[100],"CSP.":[104]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}