{"id":"https://openalex.org/W1725039148","doi":"https://doi.org/10.1145/2818375","title":"Label Cover Instances with Large Girth and the Hardness of Approximating Basic <i>k</i> -Spanner","display_name":"Label Cover Instances with Large Girth and the Hardness of Approximating Basic <i>k</i> -Spanner","publication_year":2015,"publication_date":"2015-12-31","ids":{"openalex":"https://openalex.org/W1725039148","doi":"https://doi.org/10.1145/2818375","mag":"1725039148"},"language":"en","primary_location":{"id":"doi:10.1145/2818375","is_oa":true,"landing_page_url":"https://doi.org/10.1145/2818375","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/2818375","source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://dl.acm.org/doi/pdf/10.1145/2818375","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049161363","display_name":"Michael Dinitz","orcid":"https://orcid.org/0000-0002-2632-966X"},"institutions":[{"id":"https://openalex.org/I4210101247","display_name":"American Committee for the Weizmann Institute of Science","ror":"https://ror.org/016myq798","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I4210101247"]},{"id":"https://openalex.org/I53964585","display_name":"Weizmann Institute of Science","ror":"https://ror.org/0316ej306","country_code":"IL","type":"education","lineage":["https://openalex.org/I53964585"]}],"countries":["IL","US"],"is_corresponding":false,"raw_author_name":"Michael Dinitz","raw_affiliation_strings":["Weizmann Institute of Science, Baltimore, MD","Weizmann Institute of Science, Baltimore, MD#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Weizmann Institute of Science, Baltimore, MD","institution_ids":["https://openalex.org/I4210101247"]},{"raw_affiliation_string":"Weizmann Institute of Science, Baltimore, MD#TAB#","institution_ids":["https://openalex.org/I53964585"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056370891","display_name":"Guy Kortsarz","orcid":null},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Guy Kortsarz","raw_affiliation_strings":["Rutgers University-Camden, Camden, NJ","Rutgers University-Camden, Camden, NJ#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Rutgers University-Camden, Camden, NJ","institution_ids":["https://openalex.org/I102322142"]},{"raw_affiliation_string":"Rutgers University-Camden, Camden, NJ#TAB#","institution_ids":["https://openalex.org/I102322142"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041545934","display_name":"Ran Raz","orcid":"https://orcid.org/0009-0008-1656-2258"},"institutions":[{"id":"https://openalex.org/I53964585","display_name":"Weizmann Institute of Science","ror":"https://ror.org/0316ej306","country_code":"IL","type":"education","lineage":["https://openalex.org/I53964585"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Ran Raz","raw_affiliation_strings":["Weizmann Institute of Science, Rehovot, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Weizmann Institute of Science, Rehovot, Israel","institution_ids":["https://openalex.org/I53964585"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1175,"has_fulltext":true,"cited_by_count":20,"citation_normalized_percentile":{"value":0.87296917,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"12","issue":"2","first_page":"1","last_page":"16"},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9988999962806702,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/spanner","display_name":"Spanner","score":0.9671213030815125},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7752867937088013},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7455095052719116},{"id":"https://openalex.org/keywords/girth","display_name":"Girth (graph theory)","score":0.6905878186225891},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6799148917198181},{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.6648657321929932},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.6042636632919312},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.5987780690193176},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.47241488099098206},{"id":"https://openalex.org/keywords/soundness","display_name":"Soundness","score":0.4720343351364136},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46305084228515625},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.44796022772789},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4302261471748352},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1080038845539093}],"concepts":[{"id":"https://openalex.org/C2779585601","wikidata":"https://www.wikidata.org/wiki/Q4049850","display_name":"Spanner","level":2,"score":0.9671213030815125},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7752867937088013},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7455095052719116},{"id":"https://openalex.org/C2777434295","wikidata":"https://www.wikidata.org/wiki/Q959831","display_name":"Girth (graph theory)","level":2,"score":0.6905878186225891},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6799148917198181},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.6648657321929932},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.6042636632919312},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5987780690193176},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.47241488099098206},{"id":"https://openalex.org/C39920170","wikidata":"https://www.wikidata.org/wiki/Q693083","display_name":"Soundness","level":2,"score":0.4720343351364136},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46305084228515625},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.44796022772789},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4302261471748352},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1080038845539093},{"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},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C120314980","wikidata":"https://www.wikidata.org/wiki/Q180634","display_name":"Distributed computing","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2818375","is_oa":true,"landing_page_url":"https://doi.org/10.1145/2818375","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/2818375","source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1145/2818375","is_oa":true,"landing_page_url":"https://doi.org/10.1145/2818375","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/2818375","source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2889557887","display_name":null,"funder_award_id":"45208","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"},{"id":"https://openalex.org/G5602429218","display_name":null,"funder_award_id":"434923","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8240595191","display_name":null,"funder_award_id":"452/08","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"},{"id":"https://openalex.org/G8331198436","display_name":null,"funder_award_id":"2010418","funder_id":"https://openalex.org/F4320308960","funder_display_name":"United States - Israel Binational Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320308960","display_name":"United States - Israel Binational Science Foundation","ror":"https://ror.org/00j8z2m73"},{"id":"https://openalex.org/F4320320878","display_name":"Minerva Foundation","ror":"https://ror.org/02rxjts25"},{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"},{"id":"https://openalex.org/F4320335016","display_name":"Israeli Centers for Research Excellence","ror":"https://ror.org/03w2v9593"},{"id":"https://openalex.org/F4320335375","display_name":"Planning and Budgeting Committee of the Council for Higher Education of Israel","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1725039148.pdf","grobid_xml":"https://content.openalex.org/works/W1725039148.grobid-xml"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W63101354","https://openalex.org/W1480517702","https://openalex.org/W1492237614","https://openalex.org/W1561372264","https://openalex.org/W1562956125","https://openalex.org/W1632764828","https://openalex.org/W1970259241","https://openalex.org/W1971316210","https://openalex.org/W1986144992","https://openalex.org/W1987669032","https://openalex.org/W1989274820","https://openalex.org/W1990313671","https://openalex.org/W1997369416","https://openalex.org/W1998721609","https://openalex.org/W1999032440","https://openalex.org/W2002041206","https://openalex.org/W2018963243","https://openalex.org/W2019578639","https://openalex.org/W2020400310","https://openalex.org/W2022381972","https://openalex.org/W2029772672","https://openalex.org/W2042959539","https://openalex.org/W2044989918","https://openalex.org/W2045446569","https://openalex.org/W2056403031","https://openalex.org/W2057046770","https://openalex.org/W2057994027","https://openalex.org/W2058422149","https://openalex.org/W2059453880","https://openalex.org/W2060054375","https://openalex.org/W2077824753","https://openalex.org/W2085630237","https://openalex.org/W2091569826","https://openalex.org/W2097747425","https://openalex.org/W2121615984","https://openalex.org/W2128087748","https://openalex.org/W2143996311","https://openalex.org/W2144474663","https://openalex.org/W2146522997","https://openalex.org/W2148137544","https://openalex.org/W2148352980","https://openalex.org/W2157760787","https://openalex.org/W2963693432","https://openalex.org/W4245082111"],"related_works":["https://openalex.org/W1511249877","https://openalex.org/W2950202488","https://openalex.org/W2604424424","https://openalex.org/W2993304180","https://openalex.org/W4287999588","https://openalex.org/W3082881870","https://openalex.org/W2033607935","https://openalex.org/W4388184844","https://openalex.org/W4237934402","https://openalex.org/W2081672443"],"abstract_inverted_index":{"We":[0,17],"study":[1],"the":[2,8,21,27,63,83,89,100,108,116,125,161,179,198,211,221],"well-known":[3],"Label":[4,92],"Cover":[5,93],"problem":[6,12,28,90,118,165],"under":[7],"additional":[9],"requirement":[10],"that":[11,19,144],"instances":[13],"have":[14,75],"large":[15,95,233],"girth.":[16,234],"show":[18,142],"if":[20],"girth":[22,96],"is":[23,29,114,157,196],"some":[24],"k":[25,65,110,147,163,189],",":[26,140],"roughly":[30],"2":[31,171],"log":[32,172],"1-\u03f5":[33,173],"n)/k":[34,174],"hard":[35,158],"to":[36,59,74,159,209,216,220,227,230],"approximate":[37,160],"for":[38,62,88,107,127,145],"all":[39],"constant":[40,152],"\u03f5":[41,153],"&gt;":[42,154],"0.":[43],"A":[44],"similar":[45],"theorem":[46],"was":[47,71,131],"claimed":[48],"by":[49],"Elkin":[50],"and":[51,122,150],"Peleg":[52],"[2000]":[53],"as":[54,97,99],"part":[55],"of":[56,91,104,124,184,200,213],"an":[57],"attempt":[58],"prove":[60],"hardness":[61,106,130],"basic":[64,109,162],"-spanner":[66,111,164],"problem,":[67,112],"but":[68],"their":[69],"proof":[70,103],"later":[72],"found":[73],"a":[76,167,214],"fundamental":[77],"error.":[78],"Thus,":[79],"we":[80,141],"give":[81],"both":[82,115],"first":[84,101],"nontrivial":[85],"lower":[86,182],"bound":[87,183],"with":[94],"well":[98],"full":[102],"strong":[105],"which":[113,128,206],"simplest":[117],"in":[119],"graph":[120],"spanners":[121],"one":[123],"few":[126],"super-logarithmic":[129],"not":[132],"known.":[133],"Assuming":[134],"NP":[135],"\u2286":[136],"BPTIME":[137],"(2":[138],"polylog(n)":[139],"(roughly)":[143],"every":[146,151],"\u2a7e":[148],"3":[149],"0,":[155],"it":[156],"within":[166],"factor":[168],"better":[169],"than":[170],".":[175],"This":[176,224],"improves":[177],"over":[178],"previous":[180],"best":[181],"only":[185],"\u03a9(log":[186],"n":[187],")/":[188],"from":[190],"Kortsarz":[191],"[2001].":[192],"Our":[193],"main":[194],"technique":[195],"subsampling":[197],"edges":[199],"2-query":[201],"probabilistically":[202],"checkable":[203],"proofs":[204],"(PCPs),":[205],"allows":[207],"us":[208],"reduce":[210],"degree":[212],"PCP":[215],"be":[217,228],"essentially":[218],"equal":[219],"soundness":[222],"desired.":[223],"turns":[225],"out":[226],"enough":[229],"basically":[231],"guarantee":[232]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
