{"id":"https://openalex.org/W1976090101","doi":"https://doi.org/10.1137/07070440x","title":"The Connectivity of Boolean Satisfiability: Computational and Structural Dichotomies","display_name":"The Connectivity of Boolean Satisfiability: Computational and Structural Dichotomies","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W1976090101","doi":"https://doi.org/10.1137/07070440x","mag":"1976090101"},"language":"en","primary_location":{"id":"doi:10.1137/07070440x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/07070440x","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/A5036468719","display_name":"Parikshit Gopalan","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Parikshit Gopalan","raw_affiliation_strings":["parik@cs.washington.edu#TAB#"],"affiliations":[{"raw_affiliation_string":"parik@cs.washington.edu#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041825861","display_name":"Phokion G. Kolaitis","orcid":"https://orcid.org/0000-0002-8407-8563"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Phokion G. Kolaitis","raw_affiliation_strings":["kolaitis@almaden.ibm.com and enmaneva@us.ibm.com#TAB#"],"affiliations":[{"raw_affiliation_string":"kolaitis@almaden.ibm.com and enmaneva@us.ibm.com#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078805815","display_name":"Elitza Maneva","orcid":"https://orcid.org/0000-0002-8638-1013"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Elitza Maneva","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5104056982","display_name":"Christos H. Papadimitriou","orcid":"https://orcid.org/0009-0004-6462-2316"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christos H. Papadimitriou","raw_affiliation_strings":["christos@cs.berkeley.edu#TAB#"],"affiliations":[{"raw_affiliation_string":"christos@cs.berkeley.edu#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5036468719"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.0474,"has_fulltext":false,"cited_by_count":166,"citation_normalized_percentile":{"value":0.97245137,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"38","issue":"6","first_page":"2330","last_page":"2355"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9995999932289124,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9995999932289124,"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":0.9980000257492065,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.994700014591217,"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/boolean-satisfiability-problem","display_name":"Boolean satisfiability problem","score":0.7386738657951355},{"id":"https://openalex.org/keywords/maximum-satisfiability-problem","display_name":"Maximum satisfiability problem","score":0.6621857285499573},{"id":"https://openalex.org/keywords/heuristics","display_name":"Heuristics","score":0.6107500791549683},{"id":"https://openalex.org/keywords/pspace","display_name":"PSPACE","score":0.5922548770904541},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5761516690254211},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5752825736999512},{"id":"https://openalex.org/keywords/satisfiability","display_name":"Satisfiability","score":0.5676084756851196},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.5438798069953918},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.51861971616745},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4974506199359894},{"id":"https://openalex.org/keywords/boolean-circuit","display_name":"Boolean circuit","score":0.47350814938545227},{"id":"https://openalex.org/keywords/and-inverter-graph","display_name":"And-inverter graph","score":0.45890042185783386},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.4276989996433258},{"id":"https://openalex.org/keywords/true-quantified-boolean-formula","display_name":"True quantified Boolean formula","score":0.4242139756679535},{"id":"https://openalex.org/keywords/hypercube","display_name":"Hypercube","score":0.4211440086364746},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3742520809173584},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3417811393737793},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2819681167602539},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.16407769918441772}],"concepts":[{"id":"https://openalex.org/C6943359","wikidata":"https://www.wikidata.org/wiki/Q875276","display_name":"Boolean satisfiability problem","level":2,"score":0.7386738657951355},{"id":"https://openalex.org/C111797529","wikidata":"https://www.wikidata.org/wiki/Q17080584","display_name":"Maximum satisfiability problem","level":3,"score":0.6621857285499573},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.6107500791549683},{"id":"https://openalex.org/C197685441","wikidata":"https://www.wikidata.org/wiki/Q500716","display_name":"PSPACE","level":3,"score":0.5922548770904541},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5761516690254211},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5752825736999512},{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.5676084756851196},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.5438798069953918},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.51861971616745},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4974506199359894},{"id":"https://openalex.org/C141796577","wikidata":"https://www.wikidata.org/wiki/Q837479","display_name":"Boolean circuit","level":3,"score":0.47350814938545227},{"id":"https://openalex.org/C196836630","wikidata":"https://www.wikidata.org/wiki/Q4753279","display_name":"And-inverter graph","level":4,"score":0.45890042185783386},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.4276989996433258},{"id":"https://openalex.org/C200415742","wikidata":"https://www.wikidata.org/wiki/Q1350285","display_name":"True quantified Boolean formula","level":2,"score":0.4242139756679535},{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.4211440086364746},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3742520809173584},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3417811393737793},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2819681167602539},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.16407769918441772}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/07070440x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/07070440x","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"}],"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/W67367170","https://openalex.org/W1510651616","https://openalex.org/W1518885151","https://openalex.org/W1997649256","https://openalex.org/W2018277172","https://openalex.org/W2028609790","https://openalex.org/W2034069868","https://openalex.org/W2052936500","https://openalex.org/W2055356006","https://openalex.org/W2063428816","https://openalex.org/W2068190866","https://openalex.org/W2082480388","https://openalex.org/W2085138240","https://openalex.org/W2088486516","https://openalex.org/W2091345559","https://openalex.org/W2117290960","https://openalex.org/W2150339067","https://openalex.org/W2152182443","https://openalex.org/W2621271919"],"related_works":["https://openalex.org/W4249396218","https://openalex.org/W2995617542","https://openalex.org/W4383066791","https://openalex.org/W2131164334","https://openalex.org/W2124007265","https://openalex.org/W3212751295","https://openalex.org/W3141532631","https://openalex.org/W1568384982","https://openalex.org/W1745650241","https://openalex.org/W4241989857"],"abstract_inverted_index":{"Boolean":[0,51,84,123],"satisfiability":[1,22,52],"problems":[2,53,149,194],"are":[3,195],"an":[4,204],"important":[5],"benchmark":[6],"for":[7,68,89,108,117,153,157,164,175],"questions":[8,116],"about":[9],"complexity,":[10],"algorithms,":[11],"heuristics,":[12],"and":[13,20,29,42,54,114,161,189],"threshold":[14,23],"phenomena.":[15],"Recent":[16],"work":[17],"on":[18],"heuristics":[19],"the":[21,27,32,46,62,69,74,81,90,93,97,101,109,112,118,129,133,139,158,165,176,192,210,213,217,227,230],"has":[24],"centered":[25],"around":[26],"structure":[28],"connectivity":[30,113,166,193],"of":[31,45,48,50,71,73,83,92,96,111,120,122,132,170,191,200],"solution":[33,98,218],"space.":[34,99],"Motivated":[35],"by":[36,80,216],"this":[37],"work,":[38],"we":[39,65,104],"study":[40],"structural":[41,63,223],"connectivity-related":[43],"properties":[44],"space":[47,219],"solutions":[49,82,121],"establish":[55,105],"various":[56],"dichotomies":[57,67,135],"in":[58,155,162,180,209,226],"Schaefer's":[59],"framework.":[60],"On":[61,100],"side,":[64,103],"obtain":[66],"kinds":[70],"subgraphs":[72,214,231],"hypercube":[75],"that":[76,128,208],"can":[77,172,232],"be":[78,173,233],"induced":[79,215],"formulas,":[85],"as":[86,88],"well":[87],"diameter":[91,169,188],"connected":[94],"components":[95,171],"computational":[102,134],"dichotomy":[106],"theorems":[107],"complexity":[110,190],"$st$-connectivity":[115,159],"graph":[119],"formulas.":[124],"Our":[125],"results":[126,202],"assert":[127],"intractable":[130,228],"side":[131],"is":[136,144,185,203],"PSPACE-complete,":[137],"while":[138],"tractable":[140,211],"side\u2014which":[141],"includes":[142],"but":[143],"not":[145],"limited":[146],"to":[147],"all":[148,181],"with":[150],"polynomial-time":[151],"algorithms":[152],"satisfiability\u2014is":[154],"P":[156],"question,":[160],"coNP":[163],"question.":[167],"The":[168,198],"exponential":[174],"PSPACE-complete":[177],"cases,":[178,212,229],"whereas":[179,225],"other":[182],"cases":[183],"it":[184],"linear;":[186],"thus,":[187],"remarkably":[196],"aligned.":[197],"crux":[199],"our":[201],"expressibility":[205],"theorem":[206],"showing":[207],"possess":[220],"certain":[221],"good":[222],"properties,":[224],"arbitrary.":[234]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":11},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":13},{"year":2015,"cited_by_count":20},{"year":2014,"cited_by_count":25},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":8}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}