{"id":"https://openalex.org/W2155864159","doi":"https://doi.org/10.37236/6862","title":"Large Cuts with Local Algorithms on Triangle-Free Graphs","display_name":"Large Cuts with Local Algorithms on Triangle-Free Graphs","publication_year":2017,"publication_date":"2017-10-20","ids":{"openalex":"https://openalex.org/W2155864159","doi":"https://doi.org/10.37236/6862","mag":"2155864159"},"language":"en","primary_location":{"id":"doi:10.37236/6862","doi":"https://doi.org/10.37236/6862","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6862","pdf_url":null,"source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-c","jufo-2","norway-1","oarl","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.37236/6862","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090307195","display_name":"Juho Hirvonen","orcid":"https://orcid.org/0000-0001-8268-1070","observed_orcids":["https://orcid.org/0000-0001-8268-1070"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210117673","display_name":"Institut de Recherche en Informatique Fondamentale","ror":"https://ror.org/02krdtz55","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I4210089394","https://openalex.org/I4210117673","https://openalex.org/I4210139971"]},{"id":"https://openalex.org/I4387154366","display_name":"Universit\u00e9 Paris Diderot","ror":"https://ror.org/02n7qrg46","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241","https://openalex.org/I4387154366"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Juho Hirvonen","raw_affiliation_strings":["IRIF, CNRS and University Paris Diderot","IRIF, CNRS and Univ. Paris Diderot"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IRIF, CNRS and University Paris Diderot","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210117673","https://openalex.org/I4387154366"]},{"raw_affiliation_string":"IRIF, CNRS and Univ. Paris Diderot","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210117673"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091604054","display_name":"Joel Rybicki","orcid":"https://orcid.org/0000-0002-6432-6646","observed_orcids":["https://orcid.org/0000-0002-6432-6646"]},"institutions":[{"id":"https://openalex.org/I133731052","display_name":"University of Helsinki","ror":"https://ror.org/040af2s02","country_code":"FI","type":"education","lineage":["https://openalex.org/I133731052"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Joel Rybicki","raw_affiliation_strings":["Department of Biosciences, University of Helsinki",", University of Helsinki"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Biosciences, University of Helsinki","institution_ids":["https://openalex.org/I133731052"]},{"raw_affiliation_string":", University of Helsinki","institution_ids":["https://openalex.org/I133731052"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066080641","display_name":"Stefan Schmid","orcid":"https://orcid.org/0000-0002-7798-1711","observed_orcids":["https://orcid.org/0000-0002-7798-1711"]},"institutions":[{"id":"https://openalex.org/I891191580","display_name":"Aalborg University","ror":"https://ror.org/04m5j1k67","country_code":"DK","type":"education","lineage":["https://openalex.org/I891191580"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Stefan Schmid","raw_affiliation_strings":["Department of Computer Science, Aalborg University","Aalborg university"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Aalborg University","institution_ids":["https://openalex.org/I891191580"]},{"raw_affiliation_string":"Aalborg university","institution_ids":["https://openalex.org/I891191580"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025555126","display_name":"Jukka Suomela","orcid":"https://orcid.org/0000-0001-6117-8089","observed_orcids":["https://orcid.org/0000-0001-6117-8089"]},"institutions":[{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"education","lineage":["https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Jukka Suomela","raw_affiliation_strings":["Department of Computer Science, Aalto University","Aalto Univ"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Aalto University","institution_ids":["https://openalex.org/I9927081"]},{"raw_affiliation_string":"Aalto Univ","institution_ids":["https://openalex.org/I9927081"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.8893,"has_fulltext":true,"cited_by_count":43,"citation_normalized_percentile":{"value":0.93729926,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":98},"biblio":{"volume":"24","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9106000065803528,"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":0.9106000065803528,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.07680000364780426,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.010499999858438969,"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/triangle-free-graphs","display_name":"triangle-free graphs","score":0.9819999933242798},{"id":"https://openalex.org/keywords/d-regular-graphs","display_name":"d-regular graphs","score":0.8980000019073486},{"id":"https://openalex.org/keywords/bipartite-subgraphs","display_name":"bipartite subgraphs","score":0.7919999957084656},{"id":"https://openalex.org/keywords/max-cut","display_name":"MaxCut","score":0.6499999761581421},{"id":"https://openalex.org/keywords/local-algorithms","display_name":"local algorithms","score":0.6359999775886536},{"id":"https://openalex.org/keywords/lower-bounds","display_name":"lower bounds","score":0.5540000200271606}],"concepts":[{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.636504054069519},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6126220226287842},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5229657292366028},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5210649371147156},{"id":"https://openalex.org/C165526019","wikidata":"https://www.wikidata.org/wiki/Q942557","display_name":"Maximum cut","level":3,"score":0.4910414218902588},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.4779653251171112},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.45259594917297363},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44506219029426575},{"id":"https://openalex.org/C196921405","wikidata":"https://www.wikidata.org/wiki/Q786431","display_name":"Online algorithm","level":2,"score":0.41437479853630066},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4103921055793762},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40722543001174927},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0}],"mesh":[],"locations_count":9,"locations":[{"id":"doi:10.37236/6862","doi":"https://doi.org/10.37236/6862","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6862","pdf_url":null,"source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-c","jufo-2","norway-1","oarl","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1402.2543","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1402.2543","pdf_url":"https://arxiv.org/pdf/1402.2543","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:aaltodoc.aalto.fi:123456789/29833","doi":null,"is_oa":true,"landing_page_url":"http://www.combinatorics.org/ojs/index.php/eljc/article/view/v24i4p21","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v24i4p21/pdf","source":{"id":"https://openalex.org/S4306401662","display_name":"Aaltodoc (Aalto University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I9927081","host_organization_name":"Aalto University","host_organization_lineage":["https://openalex.org/I9927081"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"mag:2155864159","doi":null,"is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1402.2543v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.696.6409","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.696.6409","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.net.t-labs.tu-berlin.de/%7Estefan/local-maxcut.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.763.7178","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.763.7178","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1402.2543.pdf","raw_type":"text"},{"id":"pmh:oai:helda.helsinki.fi:10138/228874","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/10138/228874","pdf_url":null,"source":{"id":"https://openalex.org/S4210213322","display_name":"Ty\u00f6v\u00e4entutkimus Vuosikirja","issn_l":"0784-1272","issn":["0784-1272","1459-7780"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":["ddh","jufo-1"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:pure.atira.dk:openaire/27c63ac9-8d78-4e50-85d1-79677178afb0","doi":null,"is_oa":true,"landing_page_url":"https://vbn.aau.dk/da/publications/27c63ac9-8d78-4e50-85d1-79677178afb0","pdf_url":null,"source":{"id":"https://openalex.org/S4306401731","display_name":"VBN Forskningsportal (Aalborg Universitet)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I891191580","host_organization_name":"Aalborg University","host_organization_lineage":["https://openalex.org/I891191580"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Hirvonen, J, Rybicki, J, Schmid, S & Suomela, J 2017, 'Large cuts with local algorithms on triangle-free graphs', Electronic Journal of Combinatorics, vol. 24, no. 4, #P4.21.","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1402.2543","doi":"https://doi.org/10.48550/arxiv.1402.2543","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1402.2543","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.37236/6862","doi":"https://doi.org/10.37236/6862","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6862","pdf_url":null,"source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-c","jufo-2","norway-1","oarl","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320310086","display_name":"Helsingin Yliopisto","ror":"https://ror.org/040af2s02"},{"id":"https://openalex.org/F4320321394","display_name":"Aalto-Yliopisto","ror":"https://ror.org/020hwjq30"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2155864159.pdf","grobid_xml":"https://content.openalex.org/works/W2155864159.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W155769578","https://openalex.org/W1502033971","https://openalex.org/W1564025554","https://openalex.org/W1742880224","https://openalex.org/W1970330908","https://openalex.org/W2011039300","https://openalex.org/W2021529197","https://openalex.org/W2036871172","https://openalex.org/W2038225707","https://openalex.org/W2054910423","https://openalex.org/W2087038607","https://openalex.org/W2109368894","https://openalex.org/W2138623498","https://openalex.org/W2146489710","https://openalex.org/W2404307587","https://openalex.org/W2476096155","https://openalex.org/W2482430348","https://openalex.org/W2952497148","https://openalex.org/W4235946010","https://openalex.org/W4246647751","https://openalex.org/W4299674238"],"related_works":["https://openalex.org/W2895790266","https://openalex.org/W3214063368","https://openalex.org/W3022408285","https://openalex.org/W2047159980","https://openalex.org/W7094334702","https://openalex.org/W1655511975","https://openalex.org/W2612126672","https://openalex.org/W182447659","https://openalex.org/W2163058152","https://openalex.org/W1642852375"],"abstract_inverted_index":{"Let":[0],"$G$":[1,19],"be":[2,81,159],"a":[3,16,44,55,66,84,125,134,160,182],"$d$-regular":[4,40,152,170,192],"triangle-free":[5,41,193],"graph":[6,42,128],"with":[7,20],"$m$":[8],"edges.":[9],"We":[10,116],"present":[11],"an":[12],"algorithm":[13,71,77,102,109],"which":[14],"finds":[15],"cut":[17,45,177,188],"in":[18,27,65,104,150,169],"at":[21,47],"least":[22,48],"$(1/2":[23],"+":[24],"0.28125/\\sqrt{d})m$":[25],"edges":[26,64],"expectation,":[28],"improving":[29],"upon":[30],"Shearer's":[31,75],"classic":[32,76],"result.":[33],"In":[34],"particular,":[35],"this":[36,49],"implies":[37],"that":[38,118,131,146],"any":[39,120,151,191],"has":[43],"of":[46,63,69,140,167,178,190],"size,":[50],"and":[51,78,100,142],"thus,":[52],"we":[53,172],"obtain":[54],"new":[56],"lower":[57,183],"bound":[58,184],"for":[59,119,163],"the":[60,101,165,175,186],"maximum":[61,187],"number":[62],"bipartite":[67],"subgraph":[68],"$G$.Our":[70],"is":[72,133],"simpler":[73],"than":[74],"it":[79],"can":[80,173],"interpreted":[82],"as":[83],"very":[85],"efficient":[86],"randomised":[87,108,143],"distributed":[88],"(local)":[89],"algorithm:":[90],"each":[91],"node":[92],"needs":[93],"to":[94,158,180],"produce":[95],"only":[96],"one":[97,105],"random":[98],"bit,":[99],"runs":[103],"round.":[106],"The":[107],"itself":[110],"was":[111],"discovered":[112],"using":[113],"computational":[114],"techniques.":[115],"show":[117],"fixed":[121],"$d$,":[122],"there":[123,132],"exists":[124],"weighted":[126],"neighbourhood":[127],"$\\mathcal{N}_d$":[129,141,179],"such":[130],"one-to-one":[135],"correspondence":[136],"between":[137],"heavy":[138],"cuts":[139,149,168],"local":[144],"algorithms":[145],"find":[147],"large":[148],"input":[153],"graph.":[154,194],"This":[155],"turns":[156],"out":[157],"useful":[161],"tool":[162],"analysing":[164],"existence":[166],"graphs:":[171],"compute":[174],"optimal":[176],"attain":[181],"on":[185],"size":[189]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":6},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2016-06-24T00:00:00"}