{"id":"https://openalex.org/W2005687471","doi":"https://doi.org/10.1002/rsa.3240060409","title":"Polynomial time randomized approximation schemes for Tutte\u2013Gr\u00f6thendieck invariants: The dense case","display_name":"Polynomial time randomized approximation schemes for Tutte\u2013Gr\u00f6thendieck invariants: The dense case","publication_year":1995,"publication_date":"1995-07-01","ids":{"openalex":"https://openalex.org/W2005687471","doi":"https://doi.org/10.1002/rsa.3240060409","mag":"2005687471"},"language":"en","primary_location":{"id":"doi:10.1002/rsa.3240060409","is_oa":false,"landing_page_url":"https://doi.org/10.1002/rsa.3240060409","pdf_url":null,"source":{"id":"https://openalex.org/S59667848","display_name":"Random Structures and Algorithms","issn_l":"1042-9832","issn":["1042-9832","1098-2418"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Random Structures & Algorithms","raw_type":"journal-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/A5083469386","display_name":"Noga Alon","orcid":"https://orcid.org/0000-0003-1332-4883"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Noga Alon","raw_affiliation_strings":["Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel","Department of Mathematics Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"Department of Mathematics Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056950019","display_name":"Alan Frieze","orcid":"https://orcid.org/0000-0002-8481-5615"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alan Frieze","raw_affiliation_strings":["Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213","Department of Mathematics Carnegie-Mellon University Pittsburgh - Pa 15213"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Department of Mathematics Carnegie-Mellon University Pittsburgh - Pa 15213","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090914315","display_name":"Dominic Welsh","orcid":"https://orcid.org/0000-0003-1750-219X"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Dominic Welsh","raw_affiliation_strings":["Merton College and Mathematical Institute, Oxford, United Kingdom","Merton College and Mathematical Institute, Oxford, United Kingdom#TAB#"],"affiliations":[{"raw_affiliation_string":"Merton College and Mathematical Institute, Oxford, United Kingdom","institution_ids":[]},{"raw_affiliation_string":"Merton College and Mathematical Institute, Oxford, United Kingdom#TAB#","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5083469386"],"corresponding_institution_ids":["https://openalex.org/I16391192"],"apc_list":{"value":4330,"currency":"USD","value_usd":4330},"apc_paid":null,"fwci":1.8436,"has_fulltext":false,"cited_by_count":52,"citation_normalized_percentile":{"value":0.85009346,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"6","issue":"4","first_page":"459","last_page":"478"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11476","display_name":"Graph theory and applications","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9983000159263611,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/tutte-polynomial","display_name":"Tutte polynomial","score":0.7106310129165649},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6058242917060852},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4915176331996918},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4479500651359558},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.410482794046402},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15270277857780457},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.056299030780792236}],"concepts":[{"id":"https://openalex.org/C14447369","wikidata":"https://www.wikidata.org/wiki/Q7857002","display_name":"Tutte polynomial","level":5,"score":0.7106310129165649},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6058242917060852},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4915176331996918},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4479500651359558},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.410482794046402},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15270277857780457},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.056299030780792236},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.0},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/rsa.3240060409","is_oa":false,"landing_page_url":"https://doi.org/10.1002/rsa.3240060409","pdf_url":null,"source":{"id":"https://openalex.org/S59667848","display_name":"Random Structures and Algorithms","issn_l":"1042-9832","issn":["1042-9832","1098-2418"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Random Structures & Algorithms","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","score":0.699999988079071,"display_name":"Life in Land"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W188858573","https://openalex.org/W1492445835","https://openalex.org/W1573538478","https://openalex.org/W1590167836","https://openalex.org/W1968069760","https://openalex.org/W1979446688","https://openalex.org/W2004492294","https://openalex.org/W2007746582","https://openalex.org/W2011039300","https://openalex.org/W2024710200","https://openalex.org/W2027105889","https://openalex.org/W2039763834","https://openalex.org/W2046097442","https://openalex.org/W2068033618","https://openalex.org/W2080408506","https://openalex.org/W2108932844","https://openalex.org/W2110539170","https://openalex.org/W2335132016","https://openalex.org/W3084987570","https://openalex.org/W4213257303","https://openalex.org/W6651254724"],"related_works":["https://openalex.org/W4280505073","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4387591055","https://openalex.org/W3021394452","https://openalex.org/W1718505034","https://openalex.org/W2610113778","https://openalex.org/W2170912089","https://openalex.org/W3196396437","https://openalex.org/W1998472389"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"Tutte\u2010Gr\u00f6thendieck":[2],"polynomial":[3,97],"T":[4,106],"(":[5,32,107],"G":[6,15,108,118],";":[7,109],"x":[8,33,110],",":[9,34,111,119],"y":[10,35,112],")":[11,36,113],"of":[12,41,44,49,56,66,76,78,105],"a":[13,91],"graph":[14,117,123],"encodes":[16],"numerous":[17],"interesting":[18],"combinatorial":[19],"quantities":[20],"associated":[21],"with":[22],"the":[23,31,39,45,47,54,61,67,73,103],"graph.":[24],"Its":[25],"evaluation":[26],"in":[27,30],"various":[28,70],"points":[29],"plane":[37],"give":[38],"number":[40,48,55],"spanning":[42],"forests":[43],"graph,":[46,68],"its":[50,57],"strongly":[51],"connected":[52],"orientations,":[53],"proper":[58],"k":[59],"\u2010colorings,":[60],"(all":[62],"terminal)":[63],"reliability":[64],"probability":[65],"and":[69],"other":[71],"invariants":[72],"exact":[74],"computation":[75],"each":[77],"which":[79],"is":[80],"well":[81],"known":[82],"to":[83],"be":[84],"#":[85],"P":[86],"\u2010hard.":[87],"Here":[88],"we":[89],"develop":[90],"general":[92],"technique":[93],"that":[94,120],"supplies":[95],"fully":[96],"randomised":[98],"approximation":[99],"schemes":[100],"for":[101,114],"approximating":[102],"value":[104],"any":[115,122],"dense":[116],"is,":[121],"on":[124],"n":[125],"vertices":[126],"whose":[127],"minimum.":[128]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}