{"id":"https://openalex.org/W2942215842","doi":"https://doi.org/10.1145/3313276.3316330","title":"Random walks and forbidden minors II","display_name":"Random walks and forbidden minors II","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2942215842","doi":"https://doi.org/10.1145/3313276.3316330","mag":"2942215842"},"language":"en","primary_location":{"id":"doi:10.1145/3313276.3316330","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3313276.3316330","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3313276.3316330","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing - STOC 2019","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://dl.acm.org/doi/pdf/10.1145/3313276.3316330","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100755285","display_name":"Akash Kumar","orcid":"https://orcid.org/0000-0001-7125-1737"},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Akash Kumar","raw_affiliation_strings":["Purdue University, USA"],"affiliations":[{"raw_affiliation_string":"Purdue University, USA","institution_ids":["https://openalex.org/I219193219"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038687804","display_name":"C. Seshadhri","orcid":"https://orcid.org/0000-0003-2163-3555"},"institutions":[{"id":"https://openalex.org/I185103710","display_name":"University of California, Santa Cruz","ror":"https://ror.org/03s65by71","country_code":"US","type":"education","lineage":["https://openalex.org/I185103710"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"C. Seshadhri","raw_affiliation_strings":["University of California at Santa Cruz, USA"],"affiliations":[{"raw_affiliation_string":"University of California at Santa Cruz, USA","institution_ids":["https://openalex.org/I185103710"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070103712","display_name":"Andrew Stolman","orcid":null},"institutions":[{"id":"https://openalex.org/I185103710","display_name":"University of California, Santa Cruz","ror":"https://ror.org/03s65by71","country_code":"US","type":"education","lineage":["https://openalex.org/I185103710"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andrew Stolman","raw_affiliation_strings":["University of California at Santa Cruz, USA"],"affiliations":[{"raw_affiliation_string":"University of California at Santa Cruz, USA","institution_ids":["https://openalex.org/I185103710"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100755285"],"corresponding_institution_ids":["https://openalex.org/I219193219"],"apc_list":null,"apc_paid":null,"fwci":3.1994,"has_fulltext":true,"cited_by_count":20,"citation_normalized_percentile":{"value":0.92607636,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"559","last_page":"567"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9995999932289124,"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":0.9986000061035156,"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/planarity-testing","display_name":"Planarity testing","score":0.9342581033706665},{"id":"https://openalex.org/keywords/property-testing","display_name":"Property testing","score":0.829390287399292},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.6857620477676392},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6491948962211609},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.5140196084976196},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4989809989929199},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.49610814452171326},{"id":"https://openalex.org/keywords/minor","display_name":"Minor (academic)","score":0.4783365726470947},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47763243317604065},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4708753824234009},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4115528464317322},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.26038670539855957}],"concepts":[{"id":"https://openalex.org/C68260962","wikidata":"https://www.wikidata.org/wiki/Q7200967","display_name":"Planarity testing","level":2,"score":0.9342581033706665},{"id":"https://openalex.org/C123842658","wikidata":"https://www.wikidata.org/wiki/Q2918980","display_name":"Property testing","level":2,"score":0.829390287399292},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.6857620477676392},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6491948962211609},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.5140196084976196},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4989809989929199},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.49610814452171326},{"id":"https://openalex.org/C2779760435","wikidata":"https://www.wikidata.org/wiki/Q5396169","display_name":"Minor (academic)","level":2,"score":0.4783365726470947},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47763243317604065},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4708753824234009},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4115528464317322},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.26038670539855957},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3313276.3316330","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3313276.3316330","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3313276.3316330","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing - STOC 2019","raw_type":"proceedings-article"}],"best_oa_location":{"id":"doi:10.1145/3313276.3316330","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3313276.3316330","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3313276.3316330","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing - STOC 2019","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1912567690","display_name":null,"funder_award_id":"1813165","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2305740495","display_name":null,"funder_award_id":"CCF-1813165","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2695194018","display_name":"AF: Small: Quantitative and Algorithmic Aspects of Semi-algebraic Sets and Partitions","funder_award_id":"1618981","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2854562603","display_name":null,"funder_award_id":"CCF-1740850","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3667867886","display_name":"TRIPODS: Towards a Unified Theory of Structure, Incompleteness & Uncertainty in Heterogeneous Graphs","funder_award_id":"1740850","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6203420807","display_name":null,"funder_award_id":"TRIPODS","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8716597360","display_name":null,"funder_award_id":"CCF-1618981","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2942215842.pdf","grobid_xml":"https://content.openalex.org/works/W2942215842.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W174566906","https://openalex.org/W1559116151","https://openalex.org/W1648776928","https://openalex.org/W1974544894","https://openalex.org/W1980816908","https://openalex.org/W1987374783","https://openalex.org/W1989274820","https://openalex.org/W2005079828","https://openalex.org/W2005787849","https://openalex.org/W2006450313","https://openalex.org/W2028037658","https://openalex.org/W2067016370","https://openalex.org/W2071321409","https://openalex.org/W2115589427","https://openalex.org/W2132071831","https://openalex.org/W2135512436","https://openalex.org/W2145062394","https://openalex.org/W2153822379","https://openalex.org/W2178176529","https://openalex.org/W2444233166","https://openalex.org/W2611773579","https://openalex.org/W2738460666","https://openalex.org/W2769478807","https://openalex.org/W2963670536","https://openalex.org/W4213311856","https://openalex.org/W4233246733"],"related_works":["https://openalex.org/W2982185603","https://openalex.org/W4288090301","https://openalex.org/W1978684236","https://openalex.org/W2164938550","https://openalex.org/W3003614666","https://openalex.org/W2942215842","https://openalex.org/W3043405145","https://openalex.org/W2804519719","https://openalex.org/W2024491681","https://openalex.org/W1855700180"],"abstract_inverted_index":{"Let":[0],"G":[1,23],"be":[2],"a":[3,59,79],"graph":[4],"with":[5,61,78],"n":[6],"vertices":[7],"and":[8],"maximum":[9],"degree":[10],"d.":[11],"Fix":[12],"some":[13],"minor-closed":[14],"property":[15,44,92],"P":[16,27,46],"(such":[17],"as":[18],"planarity).":[19],"We":[20],"say":[21],"that":[22,57],"is":[24,86,97],"\u03b5-far":[25],"from":[26],"if":[28],"one":[29],"has":[30],"to":[31,36,76,90],"remove":[32],"\u03b5":[33],"dn":[34],"edges":[35],"make":[37],"it":[38],"have":[39,71],"P.":[40],"The":[41],"problem":[42,89],"of":[43,53],"testing":[45],"was":[47],"introduced":[48],"in":[49,66],"the":[50,73],"seminal":[51],"work":[52],"Benjamini-Schramm-Shapira":[54],"(STOC":[55],"2008)":[56],"gave":[58],"tester":[60,75],"query":[62,83,95],"complexity":[63,96],"triply":[64],"exponential":[65],"\u03b5\u22121.":[67],"Levi-Ron":[68],"(TALG":[69],"2015)":[70],"given":[72],"best":[74],"date,":[77],"quasipolynomial":[80],"(in":[81],"\u03b5\u22121)":[82],"complexity.":[84],"It":[85],"an":[87],"open":[88],"get":[91],"testers":[93],"whose":[94],"(d\u03b5\u22121),":[98],"even":[99],"for":[100],"planarity.":[101]},"counts_by_year":[{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}