{"id":"https://openalex.org/W2036322374","doi":"https://doi.org/10.1145/1132516.1132594","title":"Integrality gaps for sparsest cut and minimum linear arrangement problems","display_name":"Integrality gaps for sparsest cut and minimum linear arrangement problems","publication_year":2006,"publication_date":"2006-05-21","ids":{"openalex":"https://openalex.org/W2036322374","doi":"https://doi.org/10.1145/1132516.1132594","mag":"2036322374"},"language":"en","primary_location":{"id":"doi:10.1145/1132516.1132594","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1132516.1132594","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/A5060217026","display_name":"Nikhil R. Devanur","orcid":"https://orcid.org/0009-0005-4406-5935"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]},{"id":"https://openalex.org/I2800444561","display_name":"Atlanta Technical College","ror":"https://ror.org/01s3vfp47","country_code":"US","type":"education","lineage":["https://openalex.org/I2800444561"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nikhil R. Devanur","raw_affiliation_strings":["Georgia Tech., Atlanta, GA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Georgia Tech., Atlanta, GA","institution_ids":["https://openalex.org/I130701444","https://openalex.org/I2800444561"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067917669","display_name":"Subhash Khot","orcid":"https://orcid.org/0009-0007-9246-4011"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]},{"id":"https://openalex.org/I2800444561","display_name":"Atlanta Technical College","ror":"https://ror.org/01s3vfp47","country_code":"US","type":"education","lineage":["https://openalex.org/I2800444561"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Subhash A. Khot","raw_affiliation_strings":["Georgia Tech., Atlanta, GA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Georgia Tech., Atlanta, GA","institution_ids":["https://openalex.org/I130701444","https://openalex.org/I2800444561"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011759026","display_name":"Rishi Saket","orcid":"https://orcid.org/0000-0002-0848-6987"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]},{"id":"https://openalex.org/I2800444561","display_name":"Atlanta Technical College","ror":"https://ror.org/01s3vfp47","country_code":"US","type":"education","lineage":["https://openalex.org/I2800444561"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rishi Saket","raw_affiliation_strings":["Georgia Tech., Atlanta, GA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Georgia Tech., Atlanta, GA","institution_ids":["https://openalex.org/I130701444","https://openalex.org/I2800444561"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063089732","display_name":"Nisheeth K. Vishnoi","orcid":"https://orcid.org/0000-0002-0255-1119"},"institutions":[{"id":"https://openalex.org/I1341412227","display_name":"IBM (United States)","ror":"https://ror.org/05hh8d621","country_code":"US","type":"company","lineage":["https://openalex.org/I1341412227"]},{"id":"https://openalex.org/I4210103279","display_name":"IBM Research - India","ror":"https://ror.org/014wt7r80","country_code":"IN","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210103279","https://openalex.org/I4210114115"]},{"id":"https://openalex.org/I68891433","display_name":"Indian Institute of Technology Delhi","ror":"https://ror.org/049tgcd06","country_code":"IN","type":"education","lineage":["https://openalex.org/I68891433"]}],"countries":["IN","US"],"is_corresponding":false,"raw_author_name":"Nisheeth K. Vishnoi","raw_affiliation_strings":["IBM India Research Lab, IIT Delhi, New Delhi","IBM India Research Lab, IIT Delhi, New Delhi#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IBM India Research Lab, IIT Delhi, New Delhi","institution_ids":["https://openalex.org/I4210103279","https://openalex.org/I68891433"]},{"raw_affiliation_string":"IBM India Research Lab, IIT Delhi, New Delhi#TAB#","institution_ids":["https://openalex.org/I1341412227"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":96,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"537","last_page":"546"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9997000098228455,"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":0.9997000098228455,"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/T12288","display_name":"Optimization and Search Problems","score":0.9923999905586243,"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/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.98089998960495,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7957439422607422},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7486312389373779},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.7266974449157715},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7168031930923462},{"id":"https://openalex.org/keywords/linear-programming-relaxation","display_name":"Linear programming relaxation","score":0.579076886177063},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.5705615282058716},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.5413119792938232},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.4960854947566986},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.47788798809051514},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.44180214405059814},{"id":"https://openalex.org/keywords/log-log-plot","display_name":"Log-log plot","score":0.4397696852684021},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4232005476951599},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.42189788818359375},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.13309764862060547},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10673671960830688},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08581498265266418}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7957439422607422},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7486312389373779},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7266974449157715},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7168031930923462},{"id":"https://openalex.org/C25360446","wikidata":"https://www.wikidata.org/wiki/Q1512771","display_name":"Linear programming relaxation","level":3,"score":0.579076886177063},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.5705615282058716},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.5413119792938232},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.4960854947566986},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.47788798809051514},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.44180214405059814},{"id":"https://openalex.org/C195292467","wikidata":"https://www.wikidata.org/wiki/Q2091879","display_name":"Log-log plot","level":3,"score":0.4397696852684021},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4232005476951599},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.42189788818359375},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.13309764862060547},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10673671960830688},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08581498265266418},{"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1132516.1132594","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1132516.1132594","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"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.5799999833106995}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1571037334","https://openalex.org/W1990313671","https://openalex.org/W2000835972","https://openalex.org/W2001020288","https://openalex.org/W2005090831","https://openalex.org/W2007525305","https://openalex.org/W2020632401","https://openalex.org/W2036322374","https://openalex.org/W2043520568","https://openalex.org/W2063491776","https://openalex.org/W2077044402","https://openalex.org/W2085427851","https://openalex.org/W2090453221","https://openalex.org/W2096746450","https://openalex.org/W2103749128","https://openalex.org/W2107881198","https://openalex.org/W2120358419","https://openalex.org/W2125703559","https://openalex.org/W2141793995","https://openalex.org/W2150148016","https://openalex.org/W2167061810","https://openalex.org/W2176446742","https://openalex.org/W2626503362"],"related_works":["https://openalex.org/W2035522910","https://openalex.org/W2005615533","https://openalex.org/W4243665620","https://openalex.org/W1529311266","https://openalex.org/W2047234016","https://openalex.org/W2052169362","https://openalex.org/W1608733163","https://openalex.org/W2623150993","https://openalex.org/W2055932080","https://openalex.org/W2065008672"],"abstract_inverted_index":{"Arora,":[0],"Rao":[1],"and":[2,64],"Vazirani":[3],"[2]":[4],"showed":[5],"that":[6,32,119],"the":[7,14,19,33,52,70,74,79,84,98,102],"standard":[8],"semi-definite":[9],"programming":[10],"(SDP)":[11],"relaxation":[12,100,109],"of":[13,27,73,78,101],"Sparsest":[15,85],"Cut":[16,86],"problem":[17,87],"with":[18],"triangle":[20],"inequality":[21],"constraints":[22],"has":[23],"an":[24,56,90],"integrality":[25,60,80,94,121],"gap":[26,34,61,81,95,122],"O(\u221alog":[28,128],"n).":[29,132],"They":[30],"conjectured":[31],"is":[35,123],"bounded":[36,124],"from":[37,125],"above":[38,126],"by":[39,54,127],"a":[40],"constant.":[41],"In":[42],"this":[43,47],"paper,":[44],"we":[45],"disprove":[46],"conjecture":[48],"(referred":[49],"to":[50],"as":[51,89],"ARV-Conjecture)":[53],"constructing":[55],"\u03a9(log":[57,91],"log":[58,92,130,131],"n)":[59,93],"instance.":[62],"Khot":[63],"Vishnoi":[65],"[16]":[66],"had":[67],"earlier":[68],"disproved":[69],"non-uniform":[71],"version":[72],"ARV-Conjecture.A":[75],"simple":[76],"\"stretching\"":[77],"instance":[82,96],"for":[83,97],"serves":[88],"SDP":[99,108],"Minimum":[103],"Linear":[104],"Arrangement":[105],"problem.":[106],"This":[107],"was":[110,117],"considered":[111],"in":[112],"[6,":[113],"11],":[114],"where":[115],"it":[116],"shown":[118],"its":[120],"n":[129]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":6}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
