{"id":"https://openalex.org/W1575897077","doi":"https://doi.org/10.1007/bfb0026095","title":"On counting and approximation","display_name":"On counting and approximation","publication_year":2005,"publication_date":"2005-11-22","ids":{"openalex":"https://openalex.org/W1575897077","doi":"https://doi.org/10.1007/bfb0026095","mag":"1575897077"},"language":"en","primary_location":{"id":"doi:10.1007/bfb0026095","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bfb0026095","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5103016415","display_name":"Johannes K\u00f6bler","orcid":"https://orcid.org/0000-0002-1215-7270"},"institutions":[{"id":"https://openalex.org/I100066346","display_name":"University of Stuttgart","ror":"https://ror.org/04vnq7t77","country_code":"DE","type":"education","lineage":["https://openalex.org/I100066346"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Johannes K\u00f6bler","raw_affiliation_strings":["Universit\u00e4t Stuttgart, Azenbergstr. 12, D7000, Stuttgart 1","Univ. Stuttgart, Stuttgart, W. Germany#TAB#"],"affiliations":[{"raw_affiliation_string":"Universit\u00e4t Stuttgart, Azenbergstr. 12, D7000, Stuttgart 1","institution_ids":["https://openalex.org/I100066346"]},{"raw_affiliation_string":"Univ. Stuttgart, Stuttgart, W. Germany#TAB#","institution_ids":["https://openalex.org/I100066346"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055009733","display_name":"Uwe Sch\u00f6ning","orcid":null},"institutions":[{"id":"https://openalex.org/I16264642","display_name":"Koblenz University of Applied Sciences","ror":"https://ror.org/04j351e79","country_code":"DE","type":"education","lineage":["https://openalex.org/I16264642"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Uwe Sch\u00f6ning","raw_affiliation_strings":["EWH Koblenz, Rheinau 3-4, D5400, Koblenz","EWH Koblenz, Koblenz, W. Germany#TAB#"],"affiliations":[{"raw_affiliation_string":"EWH Koblenz, Rheinau 3-4, D5400, Koblenz","institution_ids":["https://openalex.org/I16264642"]},{"raw_affiliation_string":"EWH Koblenz, Koblenz, W. Germany#TAB#","institution_ids":["https://openalex.org/I16264642"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027370903","display_name":"Jacobo Tor\u00e1n","orcid":"https://orcid.org/0000-0003-2168-4969"},"institutions":[{"id":"https://openalex.org/I4210134847","display_name":"Centro Tecnol\u00f3gico de Investigaci\u00f3n, Desarrollo e Innovaci\u00f3n en tecnolog\u00edas de la Informaci\u00f3n y las Comunicaciones (TIC)","ror":"https://ror.org/02s69db58","country_code":"ES","type":"nonprofit","lineage":["https://openalex.org/I4210134847"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Jacobo Toran","raw_affiliation_strings":["Facultat d'Informatica, Pau Gargallo 5, E08028, Barcelona","Facultat d'Informatica, Barcelona, Spain#TAB#"],"affiliations":[{"raw_affiliation_string":"Facultat d'Informatica, Pau Gargallo 5, E08028, Barcelona","institution_ids":[]},{"raw_affiliation_string":"Facultat d'Informatica, Barcelona, Spain#TAB#","institution_ids":["https://openalex.org/I4210134847"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5103016415"],"corresponding_institution_ids":["https://openalex.org/I100066346"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":2.4931,"has_fulltext":false,"cited_by_count":72,"citation_normalized_percentile":{"value":0.90204194,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"40","last_page":"51"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9994000196456909,"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":0.9993000030517578,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.998199999332428,"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/nondeterministic-algorithm","display_name":"Nondeterministic algorithm","score":0.5699772238731384},{"id":"https://openalex.org/keywords/oracle","display_name":"Oracle","score":0.5263617634773254},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5206441283226013},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.49484723806381226},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4829351603984833},{"id":"https://openalex.org/keywords/span","display_name":"Span (engineering)","score":0.444173663854599},{"id":"https://openalex.org/keywords/complexity-class","display_name":"Complexity class","score":0.4412819445133209},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4302509129047394},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4302336275577545},{"id":"https://openalex.org/keywords/function-approximation","display_name":"Function approximation","score":0.42820116877555847},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.42810872197151184},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.4184655249118805},{"id":"https://openalex.org/keywords/turing-machine","display_name":"Turing machine","score":0.41162770986557007},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3371031582355499},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3277931213378906},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.304057240486145},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30081337690353394},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11608678102493286},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1144038736820221},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.07790383696556091},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07678338885307312}],"concepts":[{"id":"https://openalex.org/C176181172","wikidata":"https://www.wikidata.org/wiki/Q3490301","display_name":"Nondeterministic algorithm","level":2,"score":0.5699772238731384},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.5263617634773254},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5206441283226013},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.49484723806381226},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4829351603984833},{"id":"https://openalex.org/C2778753569","wikidata":"https://www.wikidata.org/wiki/Q1960395","display_name":"Span (engineering)","level":2,"score":0.444173663854599},{"id":"https://openalex.org/C39637292","wikidata":"https://www.wikidata.org/wiki/Q908207","display_name":"Complexity class","level":3,"score":0.4412819445133209},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4302509129047394},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4302336275577545},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.42820116877555847},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.42810872197151184},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.4184655249118805},{"id":"https://openalex.org/C29248071","wikidata":"https://www.wikidata.org/wiki/Q163310","display_name":"Turing machine","level":3,"score":0.41162770986557007},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3371031582355499},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3277931213378906},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.304057240486145},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30081337690353394},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11608678102493286},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1144038736820221},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.07790383696556091},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07678338885307312},{"id":"https://openalex.org/C115903868","wikidata":"https://www.wikidata.org/wiki/Q80993","display_name":"Software engineering","level":1,"score":0.0},{"id":"https://openalex.org/C147176958","wikidata":"https://www.wikidata.org/wiki/Q77590","display_name":"Civil engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bfb0026095","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bfb0026095","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1511894390","https://openalex.org/W1560512928","https://openalex.org/W1949885173","https://openalex.org/W1975442866","https://openalex.org/W1979746590","https://openalex.org/W1984976620","https://openalex.org/W2002385864","https://openalex.org/W2006912660","https://openalex.org/W2014603110","https://openalex.org/W2018099718","https://openalex.org/W2044504659","https://openalex.org/W2051283034","https://openalex.org/W2058172107","https://openalex.org/W2065251436","https://openalex.org/W2073879013","https://openalex.org/W2077202644","https://openalex.org/W2096390054","https://openalex.org/W2115826669","https://openalex.org/W2131798840","https://openalex.org/W3111890340","https://openalex.org/W4389332570"],"related_works":["https://openalex.org/W2145906386","https://openalex.org/W1862457258","https://openalex.org/W1980326341","https://openalex.org/W2105859078","https://openalex.org/W31087064","https://openalex.org/W2122747219","https://openalex.org/W3215479332","https://openalex.org/W1978001037","https://openalex.org/W2035025857","https://openalex.org/W4387774848"],"abstract_inverted_index":null,"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}