{"id":"https://openalex.org/W2177243619","doi":"https://doi.org/10.1007/s00453-003-1073-y","title":"The Relative Complexity of Approximate Counting Problems","display_name":"The Relative Complexity of Approximate Counting Problems","publication_year":2003,"publication_date":"2003-12-10","ids":{"openalex":"https://openalex.org/W2177243619","doi":"https://doi.org/10.1007/s00453-003-1073-y","mag":"2177243619"},"language":"en","primary_location":{"id":"doi:10.1007/s00453-003-1073-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00453-003-1073-y","pdf_url":null,"source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","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/A5019297501","display_name":"Martin Dyer","orcid":"https://orcid.org/0000-0002-2018-0374"},"institutions":[{"id":"https://openalex.org/I130828816","display_name":"University of Leeds","ror":"https://ror.org/024mrxd33","country_code":"GB","type":"education","lineage":["https://openalex.org/I130828816"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Martin Dyer","raw_affiliation_strings":["School of Computing, University of Leeds,\nLeeds LS2 9JT, England"],"affiliations":[{"raw_affiliation_string":"School of Computing, University of Leeds,\nLeeds LS2 9JT, England","institution_ids":["https://openalex.org/I130828816"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029293569","display_name":"Leslie Ann Goldberg","orcid":"https://orcid.org/0000-0003-1879-6089"},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Leslie Ann Goldberg","raw_affiliation_strings":["Department of Computer Science, University of Warwick, Coventry, CV4 7AL, England"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Warwick, Coventry, CV4 7AL, England","institution_ids":["https://openalex.org/I39555362"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031194096","display_name":"Catherine Greenhill","orcid":"https://orcid.org/0000-0001-6998-2282"},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"University of Melbourne","ror":"https://ror.org/01ej9dk98","country_code":"AU","type":"education","lineage":["https://openalex.org/I165779595"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Catherine Greenhill","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Melbourne, Parkville, Australia 3010"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Melbourne, Parkville, Australia 3010","institution_ids":["https://openalex.org/I165779595"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090122841","display_name":"Mark Jerrum","orcid":"https://orcid.org/0000-0003-0863-7279"},"institutions":[{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Mark Jerrum","raw_affiliation_strings":["Division of Informatics, University of Edinburgh, JCMB, The King\u2019s Buildings, Edinburgh EH9 3JZ, Scotland","Division of Informatics, University of Edinburgh, JCMB, The King's Buildings, Edinburgh EH9 3JZ, Scotland"],"affiliations":[{"raw_affiliation_string":"Division of Informatics, University of Edinburgh, JCMB, The King\u2019s Buildings, Edinburgh EH9 3JZ, Scotland","institution_ids":["https://openalex.org/I98677209"]},{"raw_affiliation_string":"Division of Informatics, University of Edinburgh, JCMB, The King's Buildings, Edinburgh EH9 3JZ, Scotland","institution_ids":["https://openalex.org/I98677209"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5019297501","https://openalex.org/A5029293569","https://openalex.org/A5031194096","https://openalex.org/A5090122841"],"corresponding_institution_ids":["https://openalex.org/I130828816","https://openalex.org/I165779595","https://openalex.org/I39555362","https://openalex.org/I98677209"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":1.9942,"has_fulltext":false,"cited_by_count":207,"citation_normalized_percentile":{"value":0.88717761,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":100},"biblio":{"volume":"38","issue":"3","first_page":"471","last_page":"500"},"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":0.9998000264167786,"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":0.9998000264167786,"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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.9961000084877014,"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"}},{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9758999943733215,"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/theory-of-computation","display_name":"Theory of computation","score":0.7532286643981934},{"id":"https://openalex.org/keywords/complexity-class","display_name":"Complexity class","score":0.7057303190231323},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6675601005554199},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6006166934967041},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5508397817611694},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.5306169986724854},{"id":"https://openalex.org/keywords/counting-problem","display_name":"Counting problem","score":0.5303260684013367},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.5008020401000977},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46563664078712463},{"id":"https://openalex.org/keywords/subclass","display_name":"Subclass","score":0.4555964469909668},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.39854955673217773},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35562366247177124},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2746833860874176},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10848420858383179}],"concepts":[{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.7532286643981934},{"id":"https://openalex.org/C39637292","wikidata":"https://www.wikidata.org/wiki/Q908207","display_name":"Complexity class","level":3,"score":0.7057303190231323},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6675601005554199},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6006166934967041},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5508397817611694},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.5306169986724854},{"id":"https://openalex.org/C16592021","wikidata":"https://www.wikidata.org/wiki/Q5177154","display_name":"Counting problem","level":2,"score":0.5303260684013367},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.5008020401000977},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46563664078712463},{"id":"https://openalex.org/C2776194381","wikidata":"https://www.wikidata.org/wiki/Q3965271","display_name":"Subclass","level":3,"score":0.4555964469909668},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.39854955673217773},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35562366247177124},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2746833860874176},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10848420858383179},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C159654299","wikidata":"https://www.wikidata.org/wiki/Q79460","display_name":"Antibody","level":2,"score":0.0},{"id":"https://openalex.org/C203014093","wikidata":"https://www.wikidata.org/wiki/Q101929","display_name":"Immunology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00453-003-1073-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00453-003-1073-y","pdf_url":null,"source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},{"id":"pmh:oai:wrap.warwick.ac.uk:61130","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400665","display_name":"Warwick Research Archive Portal (University of Warwick)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39555362","host_organization_name":"University of Warwick","host_organization_lineage":["https://openalex.org/I39555362"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Report"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.42.9113","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.42.9113","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.dcs.warwick.ac.uk/people/academic/Leslie.Goldberg/papers/ap.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.88.5821","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.88.5821","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://web.maths.unsw.edu.au/~csg/papers/dggj-complexity.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.5299999713897705}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W22993877","https://openalex.org/W596942210","https://openalex.org/W1552288906","https://openalex.org/W1568495775","https://openalex.org/W1607251184","https://openalex.org/W1645243942","https://openalex.org/W1964821516","https://openalex.org/W1994118705","https://openalex.org/W1998076865","https://openalex.org/W2024710200","https://openalex.org/W2030087828","https://openalex.org/W2040145343","https://openalex.org/W2045281597","https://openalex.org/W2051283034","https://openalex.org/W2056262613","https://openalex.org/W2057512592","https://openalex.org/W2061042466","https://openalex.org/W2085716675","https://openalex.org/W2094500233","https://openalex.org/W2106570665","https://openalex.org/W2118547397","https://openalex.org/W2137407595","https://openalex.org/W3111890340","https://openalex.org/W3127113455"],"related_works":["https://openalex.org/W1980428853","https://openalex.org/W2247609287","https://openalex.org/W2032550399","https://openalex.org/W3094951835","https://openalex.org/W2057791178","https://openalex.org/W2964237202","https://openalex.org/W1559021700","https://openalex.org/W2743728300","https://openalex.org/W2534244659","https://openalex.org/W4293714057"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":17},{"year":2021,"cited_by_count":21},{"year":2020,"cited_by_count":15},{"year":2019,"cited_by_count":19},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":11},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":18}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
