{"id":"https://openalex.org/W153015188","doi":"https://doi.org/10.4086/toc.2006.v002a004","title":"","display_name":"","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W153015188","doi":"https://doi.org/10.4086/toc.2006.v002a004","mag":"153015188"},"language":"en","primary_location":{"id":"doi:10.4086/toc.2006.v002a004","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2006.v002a004","pdf_url":"https://theoryofcomputing.org/articles/v002a004/v002a004.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://theoryofcomputing.org/articles/v002a004/v002a004.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111965869","display_name":"Joshua Buresh-Oppenheim","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Joshua Buresh-Oppenheim","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084573067","display_name":"Nicola Galesi","orcid":"https://orcid.org/0000-0002-8522-362X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nicola Galesi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017386816","display_name":"Shlomo Hoory","orcid":"https://orcid.org/0000-0002-8166-4428"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shlomo Hoory","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043150610","display_name":"Avner Magen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Avner Magen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5003318200","display_name":"Toniann Pitassi","orcid":"https://orcid.org/0000-0002-8668-2174"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Toniann Pitassi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5111965869"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.0444,"has_fulltext":true,"cited_by_count":67,"citation_normalized_percentile":{"value":0.93505173,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"2","issue":"1","first_page":"65","last_page":"90"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998999834060669,"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":0.9998999834060669,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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":0.9945999979972839,"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/mathematical-proof","display_name":"Mathematical proof","score":0.7648656964302063},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.7472214698791504},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6860856413841248},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6347211003303528},{"id":"https://openalex.org/keywords/pigeonhole-principle","display_name":"Pigeonhole principle","score":0.5613160133361816},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4630105495452881},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4173603057861328}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.7648656964302063},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.7472214698791504},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6860856413841248},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6347211003303528},{"id":"https://openalex.org/C171988527","wikidata":"https://www.wikidata.org/wiki/Q188276","display_name":"Pigeonhole principle","level":2,"score":0.5613160133361816},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4630105495452881},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4173603057861328},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.4086/toc.2006.v002a004","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2006.v002a004","pdf_url":"https://theoryofcomputing.org/articles/v002a004/v002a004.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},{"id":"pmh:oai:iris.uniroma1.it:11573/133120","is_oa":false,"landing_page_url":"http://hdl.handle.net/11573/133120","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":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.4086/toc.2006.v002a004","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2006.v002a004","pdf_url":"https://theoryofcomputing.org/articles/v002a004/v002a004.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W153015188.pdf","grobid_xml":"https://content.openalex.org/works/W153015188.grobid-xml"},"referenced_works_count":42,"referenced_works":["https://openalex.org/W152703237","https://openalex.org/W1499875748","https://openalex.org/W1568620904","https://openalex.org/W1587123489","https://openalex.org/W1867057885","https://openalex.org/W1893254807","https://openalex.org/W1951390451","https://openalex.org/W1972894929","https://openalex.org/W1985123706","https://openalex.org/W1996256832","https://openalex.org/W1999032440","https://openalex.org/W1999522767","https://openalex.org/W2009683816","https://openalex.org/W2011805810","https://openalex.org/W2020632401","https://openalex.org/W2026189949","https://openalex.org/W2038193643","https://openalex.org/W2044095368","https://openalex.org/W2062897452","https://openalex.org/W2069767473","https://openalex.org/W2088844265","https://openalex.org/W2093624290","https://openalex.org/W2100440346","https://openalex.org/W2104727719","https://openalex.org/W2106264302","https://openalex.org/W2113462655","https://openalex.org/W2117749206","https://openalex.org/W2122055721","https://openalex.org/W2126362918","https://openalex.org/W2126420408","https://openalex.org/W2130847546","https://openalex.org/W2132489129","https://openalex.org/W2133392939","https://openalex.org/W2133527541","https://openalex.org/W2145243417","https://openalex.org/W2146823188","https://openalex.org/W2167508847","https://openalex.org/W2210840110","https://openalex.org/W2566335580","https://openalex.org/W2611147814","https://openalex.org/W4238671349","https://openalex.org/W4245630182"],"related_works":["https://openalex.org/W4288055874","https://openalex.org/W2165390183","https://openalex.org/W2068071783","https://openalex.org/W1974091179","https://openalex.org/W2183083419","https://openalex.org/W4301376359","https://openalex.org/W1754605724","https://openalex.org/W4287811509","https://openalex.org/W3022132071","https://openalex.org/W3177600251"],"abstract_inverted_index":{"We":[0,32],"present":[1],"a":[2,75],"new":[3,40],"method":[4,35],"for":[5,10,30,48,53],"proving":[6],"rank":[7,46,107,116,126,133],"lower":[8,72],"bounds":[9,47,73],"the":[11,38,64,88,96,124,131,139],"cutting":[12],"planes":[13],"procedures":[14,84],"of":[15,78,80,141],"Gomory":[16],"and":[17,20,22,50,63,109],"Chvtal":[18],"(GC)":[19],"Lovsz":[21],"Schrijver":[23],"(LS),":[24],"when":[25,85],"viewed":[26],"as":[27],"proof":[28],"systems":[29],"unsatisfiability.":[31],"apply":[33],"this":[34],"to":[36,87],"obtain":[37],"following":[39],"results:":[41],"First,":[42],"we":[43,100,120,137],"prove":[44],"near-optimal":[45],"GC":[49,81,108,125],"LS":[51,83,110,132],"proofs":[52,111],"several":[54],"prominent":[55],"unsatisfiable":[56,102],"CNF":[57],"examples,":[58],"including":[59],"random":[60],"kCNF":[61],"formulas":[62],"Tseitin":[65],"graph":[66],"formulas.":[67],"It":[68],"follows":[69],"from":[70],"these":[71],"that":[74,104,113],"linear":[76,91,115],"number":[77],"rounds":[79],"or":[82],"applied":[86],"standard":[89],"MAXSAT":[90],"relaxation":[92],"does":[93],"not":[94],"reduce":[95],"integrality":[97],"gap.":[98],"Second,":[99],"give":[101,121],"examples":[103,122],"have":[105],"constant":[106],"but":[112,130],"require":[114],"Resolution":[117],"proofs.":[118],"Third,":[119],"where":[123],"is":[127,134],"O(log":[128],"n)":[129],"linear.":[135],"Finally,":[136],"address":[138],"question":[140],"size":[142]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":27},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":4}],"updated_date":"2026-05-03T08:25:01.440150","created_date":"2016-06-24T00:00:00"}