{"id":"https://openalex.org/W2152982698","doi":"https://doi.org/10.1145/2591796.2591813","title":"Polynomial bounds for the grid-minor theorem","display_name":"Polynomial bounds for the grid-minor theorem","publication_year":2014,"publication_date":"2014-05-31","ids":{"openalex":"https://openalex.org/W2152982698","doi":"https://doi.org/10.1145/2591796.2591813","mag":"2152982698"},"language":"en","primary_location":{"id":"doi:10.1145/2591796.2591813","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2591796.2591813","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the forty-sixth annual ACM symposium on Theory of computing","raw_type":"proceedings-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/A5036503505","display_name":"Chandra Chekuri","orcid":"https://orcid.org/0000-0003-3035-1699"},"institutions":[{"id":"https://openalex.org/I2801919071","display_name":"University of Illinois System","ror":"https://ror.org/05e94g991","country_code":"US","type":"education","lineage":["https://openalex.org/I2801919071"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Chandra Chekuri","raw_affiliation_strings":["University of Illinois, Urbana, IL"],"affiliations":[{"raw_affiliation_string":"University of Illinois, Urbana, IL","institution_ids":["https://openalex.org/I2801919071"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056023203","display_name":"Julia Chuzhoy","orcid":"https://orcid.org/0000-0001-7839-751X"},"institutions":[{"id":"https://openalex.org/I160992636","display_name":"Toyota Technological Institute at Chicago","ror":"https://ror.org/02sn5gb64","country_code":"US","type":"education","lineage":["https://openalex.org/I160992636"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Julia Chuzhoy","raw_affiliation_strings":["Toyota Technological Institute at Chicago, Chicago, IL"],"affiliations":[{"raw_affiliation_string":"Toyota Technological Institute at Chicago, Chicago, IL","institution_ids":["https://openalex.org/I160992636"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5036503505"],"corresponding_institution_ids":["https://openalex.org/I2801919071"],"apc_list":null,"apc_paid":null,"fwci":19.3755,"has_fulltext":false,"cited_by_count":72,"citation_normalized_percentile":{"value":0.99593536,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"60","last_page":"69"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","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/T10374","display_name":"Advanced Graph Theory Research","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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9994999766349792,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9993000030517578,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/treewidth","display_name":"Treewidth","score":0.9277324676513672},{"id":"https://openalex.org/keywords/graph-minor","display_name":"Graph minor","score":0.831012487411499},{"id":"https://openalex.org/keywords/minor","display_name":"Minor (academic)","score":0.8189101219177246},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7339884638786316},{"id":"https://openalex.org/keywords/robertson\u2013seymour-theorem","display_name":"Robertson\u2013Seymour theorem","score":0.6947239637374878},{"id":"https://openalex.org/keywords/tree-decomposition","display_name":"Tree decomposition","score":0.6164344549179077},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6156787872314453},{"id":"https://openalex.org/keywords/partial-k-tree","display_name":"Partial k-tree","score":0.5880988240242004},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5546694993972778},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4885905683040619},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.4624716341495514},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.45978787541389465},{"id":"https://openalex.org/keywords/tree-depth","display_name":"Tree-depth","score":0.4492718279361725},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.42710012197494507},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.3447777330875397},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.2842392325401306},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.14810046553611755},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.07896575331687927},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06203615665435791},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.05773252248764038}],"concepts":[{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.9277324676513672},{"id":"https://openalex.org/C140752511","wikidata":"https://www.wikidata.org/wiki/Q905837","display_name":"Graph minor","level":5,"score":0.831012487411499},{"id":"https://openalex.org/C2779760435","wikidata":"https://www.wikidata.org/wiki/Q5396169","display_name":"Minor (academic)","level":2,"score":0.8189101219177246},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7339884638786316},{"id":"https://openalex.org/C173644813","wikidata":"https://www.wikidata.org/wiki/Q3527155","display_name":"Robertson\u2013Seymour theorem","level":5,"score":0.6947239637374878},{"id":"https://openalex.org/C70501317","wikidata":"https://www.wikidata.org/wiki/Q462095","display_name":"Tree decomposition","level":5,"score":0.6164344549179077},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6156787872314453},{"id":"https://openalex.org/C128764233","wikidata":"https://www.wikidata.org/wiki/Q7140374","display_name":"Partial k-tree","level":5,"score":0.5880988240242004},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5546694993972778},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4885905683040619},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.4624716341495514},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.45978787541389465},{"id":"https://openalex.org/C69284658","wikidata":"https://www.wikidata.org/wiki/Q7837500","display_name":"Tree-depth","level":5,"score":0.4492718279361725},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.42710012197494507},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.3447777330875397},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.2842392325401306},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.14810046553611755},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.07896575331687927},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06203615665435791},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.05773252248764038},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/2591796.2591813","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2591796.2591813","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the forty-sixth annual ACM symposium on Theory of computing","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.385.8105","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.385.8105","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://ttic.uchicago.edu/~cjulia/papers/improved-GMT.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6448516009","display_name":null,"funder_award_id":"CCF-1016684, CCF-1319376, CCF-0844872, CCF-1318242","funder_id":"https://openalex.org/F4320337387","funder_display_name":"Division of Computing and Communication Foundations"}],"funders":[{"id":"https://openalex.org/F4320306151","display_name":"Alfred P. Sloan Foundation","ror":"https://ror.org/052csg198"},{"id":"https://openalex.org/F4320337387","display_name":"Division of Computing and Communication Foundations","ror":"https://ror.org/01mng8331"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W132145278","https://openalex.org/W748479430","https://openalex.org/W1551708885","https://openalex.org/W1577694003","https://openalex.org/W1751846631","https://openalex.org/W1786780942","https://openalex.org/W1972100851","https://openalex.org/W1976463682","https://openalex.org/W1978207220","https://openalex.org/W1979444789","https://openalex.org/W1984361668","https://openalex.org/W1989274820","https://openalex.org/W1999867351","https://openalex.org/W2009946412","https://openalex.org/W2011334641","https://openalex.org/W2019041817","https://openalex.org/W2033480692","https://openalex.org/W2057826895","https://openalex.org/W2068115726","https://openalex.org/W2069159763","https://openalex.org/W2078013954","https://openalex.org/W2085348754","https://openalex.org/W2088844265","https://openalex.org/W2100346402","https://openalex.org/W2145818650","https://openalex.org/W2150148016","https://openalex.org/W2157421865","https://openalex.org/W2158584754","https://openalex.org/W2165303918","https://openalex.org/W2170380135","https://openalex.org/W2584961879","https://openalex.org/W2949739362","https://openalex.org/W2952707850","https://openalex.org/W3039948875","https://openalex.org/W6682309212","https://openalex.org/W6683266292"],"related_works":["https://openalex.org/W1836127928","https://openalex.org/W2027388354","https://openalex.org/W1490290385","https://openalex.org/W83147424","https://openalex.org/W2275773863","https://openalex.org/W2968633427","https://openalex.org/W2152982698","https://openalex.org/W2033480692","https://openalex.org/W2563767922","https://openalex.org/W4285473334"],"abstract_inverted_index":{"One":[0],"of":[1,66,73,87,160],"the":[2,15,20,59,104,120],"key":[3],"results":[4],"in":[5,51,151,164],"Robertson":[6],"and":[7,54,89,92,94,126,142,154],"Seymour's":[8],"seminal":[9],"work":[10,86],"on":[11],"graph":[12,34,52,65],"minors":[13],"is":[14,37,149],"Grid-Minor":[16],"Theorem":[17],"(also":[18],"called":[19],"Excluded":[21],"Grid":[22],"Theorem).":[23],"The":[24,78],"theorem":[25,46],"states":[26],"that":[27,63,98,110,131,156],"for":[28,135],"every":[29,33,64],"fixed-size":[30],"grid":[31,71],"H,":[32],"whose":[35,146],"treewidth":[36,67,125],"large":[38],"enough,":[39],"contains":[40,69],"H":[41],"as":[42],"a":[43,70,158,162],"minor.":[44],"This":[45],"has":[47],"found":[48],"many":[49],"applications":[50],"theory":[53],"algorithms.":[55],"Let":[56],"f(k)":[57,75,99,111,132],"denote":[58],"largest":[60],"value,":[61],"such":[62,161],"k":[68],"minor":[72],"size":[74,128],"\u00d7":[76],"f(k).":[77],"best":[79,105],"current":[80],"quantitative":[81],"bound,":[82],"due":[83],"to":[84],"recent":[85],"Kawarabayashi":[88],"Kobayashi":[90],"[15],":[91],"Leaf":[93],"Seymour":[95],"[18],":[96],"shows":[97],"=":[100,112,133],"\u03a9(\u221alogk/loglogk).":[101],"In":[102,115],"contrast,":[103],"known":[106],"upper":[107],"bound":[108],"implies":[109],"O(\u221ak/logk)":[113],"[22].":[114],"this":[116],"paper":[117],"we":[118],"obtain":[119],"first":[121],"polynomial":[122,150],"relationship":[123],"between":[124],"grid-minor":[127,163],"by":[129],"showing":[130],"\u03a9(k\u03b4)":[134],"some":[136],"fixed":[137],"constant":[138],"\u03b4":[139],">":[140],"0,":[141],"describe":[143],"an":[144],"algorithm,":[145],"running":[147],"time":[148],"|V":[152],"(G)|":[153],"k,":[155],"finds":[157],"model":[159],"G.":[165]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":12},{"year":2016,"cited_by_count":17},{"year":2015,"cited_by_count":13},{"year":2014,"cited_by_count":11},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
